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Probabilistic inference offers a principled framework for understanding both behaviour and cortical computation. However, two basic and ubiquitous properties of cortical responses seem difficult to reconcile with probabilistic inference: neural activity displays prominent oscillations in response to constant input, and large transient changes in response to stimulus onset. Here we show that these dynamical behaviours may in fact be understood as hallmarks of the specific representation and algorithm that the cortex employs to perform probabilistic inference. We demonstrate that a particular family of probabilistic inference algorithms, Hamiltonian Monte Carlo (HMC), naturally maps onto the dynamics of excitatory-inhibitory neural networks. Specifically, we constructed a model of an excitatory-inhibitory circuit in primary visual cortex that performed HMC inference, and thus inherently gave rise to oscillations and transients. These oscillations were not mere epiphenomena but served an important functional role: speeding up inference by rapidly spanning a large volume of state space. Inference thus became an order of magnitude more efficient than in a non-oscillatory variant of the model. In addition, the network matched two specific properties of observed neural dynamics that would otherwise be difficult to account for in the context of probabilistic inference. First, the frequency of oscillations as well as the magnitude of transients increased with the contrast of the image stimulus. Second, excitation and inhibition were balanced, and inhibition lagged excitation. These results suggest a new functional role for the separation of cortical populations into excitatory and inhibitory neurons, and for the neural oscillations that emerge in such excitatory-inhibitory networks: enhancing the efficiency of cortical computations.

Probabilistic Latent Tensor Factorization (PLTF) is a recently proposed probabilistic framework for modelling multi-way data. Not only the common tensor factorization models but also any arbitrary tensor factorization structure can be realized by the PLTF framework. This paper presents full Bayesian inference via variational Bayes that facilitates more powerful modelling and allows more sophisticated inference on the PLTF framework. We illustrate our approach on model order selection and link prediction.

The distribution semantics is one of the most prominent approaches for the combination of logic programming and probability theory. Many languages follow this semantics, such as Independent Choice Logic, PRISM, pD, Logic Programs with Annotated Disjunctions (LPADs) and ProbLog. When a program contains functions symbols, the distribution semantics is well-defined only if the set of explanations for a query is finite and so is each explanation. Well-definedness is usually either explicitly imposed or is achieved by severely limiting the class of allowed programs. In this paper we identify a larger class of programs for which the semantics is well-defined together with an efficient procedure for computing the probability of queries. Since LPADs offer the most general syntax, we present our results for them, but our results are applicable to all languages under the distribution semantics. We present the algorithm "Probabilistic Inference with Tabling and Answer subsumption" (PITA) that computes the probability of queries by transforming a probabilistic program into a normal program and then applying SLG resolution with answer subsumption. PITA has been implemented in XSB and tested on six domains: two with function symbols and four without. The execution times are compared with those of ProbLog, cplint and CVE, PITA was almost always able to solve larger problems in a shorter time, on domains with and without function symbols.

The use of standard statistical methods, such as maximum likelihood, is often justified based on their asymptotic properties. For suitably regular models, this theory is standard but, when the model is non-regular, e.g., the support depends on the parameter, these asymptotic properties may be difficult to assess. Recently, an inferential model (IM) framework has been developed that provides valid prior-free probabilistic inference without the need for asymptotic justification. In this paper, we construct an IM for a class of highly non-regular models with parameter-dependent support. This construction requires conditioning, which is facilitated through the solution of a particular differential equation. We prove that the plausibility intervals derived from this IM are exact confidence intervals, and we demonstrate their efficiency in a simulation study.

Non-deductive reasoning systems are often {\em representation dependent}: representing the same situation in two different ways may cause such a system to return two different answers. Some have viewed this as a significant problem. For example, the principle of maximum entropy has been subjected to much criticism due to its representation dependence. There has, however, been almost no work investigating representation dependence. In this paper, we formalize this notion and show that it is not a problem specific to maximum entropy. In fact, we show that any representation-independent probabilistic inference procedure that ignores irrelevant information is essentially entailment, in a precise sense. Moreover, we show that representation independence is incompatible with even a weak default assumption of independence. We then show that invariance under a restricted class of representation changes can form a reasonable compromise between representation independence and other desiderata, and provide a construction of a family of inference procedures that provides such restricted representation independence, using relative entropy.

This article is from Journal of Psychopharmacology (Oxford, England) , volume 26 . Abstract Evidence suggests that some aspects of schizophrenia can be induced in healthy volunteers through acute administration of the non-competitive NMDA-receptor antagonist, ketamine. In probabilistic inference tasks, patients with schizophrenia have been shown to ‘jump to conclusions’ (JTC) when asked to make a decision. We aimed to test whether healthy participants receiving ketamine would adopt a JTC response pattern resembling that of patients. The paradigmatic task used to investigate JTC has been the ‘urn’ task, where participants are shown a sequence of beads drawn from one of two ‘urns’, each containing coloured beads in different proportions. Participants make a decision when they think they know the urn from which beads are being drawn. We compared performance on the urn task between controls receiving acute ketamine or placebo with that of patients with schizophrenia and another group of controls matched to the patient group. Patients were shown to exhibit a JTC response pattern relative to their matched controls, whereas JTC was not evident in controls receiving ketamine relative to placebo. Ketamine does not appear to promote JTC in healthy controls, suggesting that ketamine does not affect probabilistic inferences.

Linear mixed-effect models with two variance components are often used when variability comes from two sources. In genetics applications, variation in observed traits can be attributed to biological and environmental effects, and the heritability coefficient is a fundamental quantity that measures the proportion of total variability due to the biological effect. We propose a new inferential model approach which yields exact prior-free probabilistic inference on the heritability coefficient. In particular we construct exact confidence intervals and demonstrate numerically our method's efficiency compared to that of existing methods.

The means by which cortical neural networks are able to efficiently solve inference problems remains an open question in computational neuroscience. Recently, abstract models of Bayesian computation in neural circuits have been proposed, but they lack a mechanistic interpretation at the single-cell level. In this article, we describe a complete theoretical framework for building networks of leaky integrate-and-fire neurons that can sample from arbitrary probability distributions over binary random variables. We test our framework for a model inference task based on a psychophysical phenomenon (the Knill-Kersten optical illusion) and further assess its performance when applied to randomly generated distributions. As the local computations performed by the network strongly depend on the interaction between neurons, we compare several types of couplings mediated by either single synapses or interneuron chains. Due to its robustness to substrate imperfections such as parameter noise and background noise correlations, our model is particularly interesting for implementation on novel, neuro-inspired computing architectures, which can thereby serve as a fast, low-power substrate for solving real-world inference problems.

The Hilbert space of probability mass functions (pmf) is introduced in this thesis. A factorization method for multivariate pmfs is proposed by using the tools provided by the Hilbert space of pmfs. The resulting factorization is special for two reasons. First, it reveals the algebraic relations between the involved random variables. Second, it determines the conditional independence relations between the random variables. Due to the first property of the resulting factorization, it can be shown that channel decoders can be employed in the solution of probabilistic inference problems other than decoding. This approach might lead to new probabilistic inference algorithms and new hardware options for the implementation of these algorithms. An example of new inference algorithms inspired by the idea of using channel decoder for other inference tasks is a multiple-input multiple-output (MIMO) detection algorithm which has a complexity of the square-root of the optimum MIMO detection algorithm.

Reasoning on large and complex real-world models is a computationally difficult task, yet one that is required for effective use of many AI applications. A plethora of inference algorithms have been developed that work well on specific models or only on parts of general models. Consequently, a system that can intelligently apply these inference algorithms to different parts of a model for fast reasoning is highly desirable. We introduce a new framework called structured factored inference (SFI) that provides the foundation for such a system. Using models encoded in a probabilistic programming language, SFI provides a sound means to decompose a model into sub-models, apply an inference algorithm to each sub-model, and combine the resulting information to answer a query. Our results show that SFI is nearly as accurate as exact inference yet retains the benefits of approximate inference methods.

Robust environment perception is essential for decision-making on robots operating in complex domains. Principled treatment of uncertainty sources in a robot's observation model is necessary for accurate mapping and object detection. This is important not only for low-level observations (e.g., accelerometer data), but for high-level observations such as semantic object labels as well. This paper presents an approach for filtering sequences of object classification probabilities using online modeling of the noise characteristics of the classifier outputs. A hierarchical Bayesian approach is used to model per-class noise distributions, while simultaneously allowing sharing of high-level noise characteristics between classes. The proposed filtering scheme, called Hierarchical Bayesian Noise Inference (HBNI), is shown to outperform classification accuracy of existing methods. The paper also presents real-time filtered classification hardware experiments running fully onboard a moving quadrotor, where the proposed approach is demonstrated to work in a challenging domain where noise-agnostic filtering fails.

Many application domains such as ecology or genomics have to deal with multivariate non Gaussian observations. A typical example is the joint observation of the respective abundances of a set of species in a series of sites, aiming to understand the co-variations between these species. The Gaussian setting provides a canonical way to model such dependencies, but does not apply in general. We consider here the multivariate exponential family framework for which we introduce a generic model with multivariate Gaussian latent variables. We show that approximate maximum likelihood inference can be achieved via a variational algorithm for which gradient descent easily applies. We show that this setting enables us to account for covariates and offsets. We then focus on the case of the Poisson-lognormal model in the context of community ecology.

This article is from PLoS ONE , volume 9 . Abstract Exact Bayesian inference can sometimes be performed efficiently for special cases where a function has commutative and associative symmetry of its inputs (called “causal independence”). For this reason, it is desirable to exploit such symmetry on big data sets. Here we present a method to exploit a general form of this symmetry on probabilistic adder nodes by transforming those probabilistic adder nodes into a probabilistic convolution tree with which dynamic programming computes exact probabilities. A substantial speedup is demonstrated using an illustration example that can arise when identifying splice forms with bottom-up mass spectrometry-based proteomics. On this example, even state-of-the-art exact inference algorithms require a runtime more than exponential in the number of splice forms considered. By using the probabilistic convolution tree, we reduce the runtime to and the space to where is the number of variables joined by an additive or cardinal operator. This approach, which can also be used with junction tree inference, is applicable to graphs with arbitrary dependency on counting variables or cardinalities and can be used on diverse problems and fields like forward error correcting codes, elemental decomposition, and spectral demixing. The approach also trivially generalizes to multiple dimensions.

This article is from Frontiers in Synaptic Neuroscience , volume 6 . Abstract Learning and memory operations in neural circuits are believed to involve molecular cascades of synaptic and nonsynaptic changes that lead to a diverse repertoire of dynamical phenomena at higher levels of processing. Hebbian and homeostatic plasticity, neuromodulation, and intrinsic excitability all conspire to form and maintain memories. But it is still unclear how these seemingly redundant mechanisms could jointly orchestrate learning in a more unified system. To this end, a Hebbian learning rule for spiking neurons inspired by Bayesian statistics is proposed. In this model, synaptic weights and intrinsic currents are adapted on-line upon arrival of single spikes, which initiate a cascade of temporally interacting memory traces that locally estimate probabilities associated with relative neuronal activation levels. Trace dynamics enable synaptic learning to readily demonstrate a spike-timing dependence, stably return to a set-point over long time scales, and remain competitive despite this stability. Beyond unsupervised learning, linking the traces with an external plasticity-modulating signal enables spike-based reinforcement learning. At the postsynaptic neuron, the traces are represented by an activity-dependent ion channel that is shown to regulate the input received by a postsynaptic cell and generate intrinsic graded persistent firing levels. We show how spike-based Hebbian-Bayesian learning can be performed in a simulated inference task using integrate-and-fire (IAF) neurons that are Poisson-firing and background-driven, similar to the preferred regime of cortical neurons. Our results support the view that neurons can represent information in the form of probability distributions, and that probabilistic inference could be a functional by-product of coupled synaptic and nonsynaptic mechanisms operating over several timescales. The model provides a biophysical realization of Bayesian computation by reconciling several observed neural phenomena whose functional effects are only partially understood in concert.

We propose a novel sampling framework for inference in probabilistic models: an active learning approach that converges more quickly (in wall-clock time) than Markov chain Monte Carlo (MCMC) benchmarks. The central challenge in probabilistic inference is numerical integration, to average over ensembles of models or unknown (hyper-)parameters (for example to compute the marginal likelihood or a partition function). MCMC has provided approaches to numerical integration that deliver state-of-the-art inference, but can suffer from sample inefficiency and poor convergence diagnostics. Bayesian quadrature techniques offer a model-based solution to such problems, but their uptake has been hindered by prohibitive computation costs. We introduce a warped model for probabilistic integrands (likelihoods) that are known to be non-negative, permitting a cheap active learning scheme to optimally select sample locations. Our algorithm is demonstrated to offer faster convergence (in seconds) relative to simple Monte Carlo and annealed importance sampling on both synthetic and real-world examples.

This paper proposes a new approach for approximate evaluation of #P-hard queries with probabilistic databases. In our approach, every query is evaluated entirely in the database engine by evaluating a fixed number of query plans, each providing an upper bound on the true probability, then taking their minimum. We provide an algorithm that takes into account important schema information to enumerate only the minimal necessary plans among all possible plans. Importantly, this algorithm is a strict generalization of all known results of PTIME self-join-free conjunctive queries: A query is safe if and only if our algorithm returns one single plan. We also apply three relational query optimization techniques to evaluate all minimal safe plans very fast. We give a detailed experimental evaluation of our approach and, in the process, provide a new way of thinking about the value of probabilistic methods over non-probabilistic methods for ranking query answers.

Detection of point sources in images is a fundamental operation in astrophysics, and is crucial for constraining population models of the underlying point sources or characterizing the background emission. Standard techniques fall short in the crowded-field limit, losing sensitivity to faint sources and failing to track their covariance with close neighbors. We construct a Bayesian framework to perform inference of faint or overlapping point sources. The method involves probabilistic cataloging, where samples are taken from the posterior probability distribution of catalogs consistent with an observed photon count map. In order to validate our method we sample random catalogs of the gamma-ray sky in the direction of the North Galactic Pole (NGP) by binning the data in energy and Point Spread Function (PSF) classes. Using three energy bins spanning $0.3 - 1$, $1 - 3$ and $3 - 10$ GeV, we identify $270\substack{+30 \\ -10}$ point sources inside a $40^\circ \times 40^\circ$ region around the NGP above our point-source inclusion limit of $3 \times 10^{-11}$/cm$^2$/s/sr/GeV at the $1-3$ GeV energy bin. Modeling the flux distribution as a power law, we infer the slope to be $-1.92\substack{+0.07 \\ -0.05}$ and estimate the contribution of point sources to the total emission as $18\substack{+2 \\ -2}$\%. These uncertainties in the flux distribution are fully marginalized over the number as well as the spatial and spectral properties of the unresolved point sources. This marginalization allows a robust test of whether the apparently isotropic emission in an image is due to unresolved point sources or of truly diffuse origin.

In this paper, we consider the problem of lifted inference in the context of Prism-like probabilistic logic programming languages. Traditional inference in such languages involves the construction of an explanation graph for the query and computing probabilities over this graph. When evaluating queries over probabilistic logic programs with a large number of instances of random variables, traditional methods treat each instance separately. For many programs and queries, we observe that explanations can be summarized into substantially more compact structures, which we call lifted explanation graphs. In this paper, we define lifted explanation graphs and operations over them. In contrast to existing lifted inference techniques, our method for constructing lifted explanations naturally generalizes existing methods for constructing explanation graphs. To compute probability of query answers, we solve recurrences generated from the lifted graphs. We show examples where the use of our technique reduces the asymptotic complexity of inference.

We present a probabilistic model for constraint-based grammars and a method for estimating the parameters of such models from incomplete, i.e., unparsed data. Whereas methods exist to estimate the parameters of probabilistic context-free grammars from incomplete data (Baum 1970), so far for probabilistic grammars involving context-dependencies only parameter estimation techniques from complete, i.e., fully parsed data have been presented (Abney 1997). However, complete-data estimation requires labor-intensive, error-prone, and grammar-specific hand-annotating of large language corpora. We present a log-linear probability model for constraint logic programming, and a general algorithm to estimate the parameters of such models from incomplete data by extending the estimation algorithm of Della-Pietra, Della-Pietra, and Lafferty (1997) to incomplete data settings.

This article is from Nucleic Acids Research , volume 41 . Abstract Using nuclear factor-κB (NF-κB) ChIP-Seq data, we present a framework for iterative learning of regulatory networks. For every possible transcription factor-binding site (TFBS)-putatively regulated gene pair, the relative distance and orientation are calculated to learn which TFBSs are most likely to regulate a given gene. Weighted TFBS contributions to putative gene regulation are integrated to derive an NF-κB gene network. A de novo motif enrichment analysis uncovers secondary TFBSs (AP1, SP1) at characteristic distances from NF-κB/RelA TFBSs. Comparison with experimental ENCODE ChIP-Seq data indicates that experimental TFBSs highly correlate with predicted sites. We observe that RelA-SP1-enriched promoters have distinct expression profiles from that of RelA-AP1 and are enriched in introns, CpG islands and DNase accessible sites. Sixteen novel NF-κB/RelA-regulated genes and TFBSs were experimentally validated, including TANK, a negative feedback gene whose expression is NF-κB/RelA dependent and requires a functional interaction with the AP1 TFBSs. Our probabilistic method yields more accurate NF-κB/RelA-regulated networks than a traditional, distance-based approach, confirmed by both analysis of gene expression and increased informativity of Genome Ontology annotations. Our analysis provides new insights into how co-occurring TFBSs and local chromatin context orchestrate activation of NF-κB/RelA sub-pathways differing in biological function and temporal expression patterns.

Ambiguity results from having limited knowledge of the process that generates outcomes. It is argued that many real-world processes are perceived to be ambiguous; moreover, as Ellsberg demonstrated, this poses problems for theories of probability operationalized via choices amongst gambles. A descriptive model of how people make judgments under ambiguity in tasks where data come from a source of limited, but not exactly known reliability, is proposed. The model assumes an anchoring-and-adjustment process in which data provides the anchor, and adjustments are made for what might have been. The latter is modeled as the result of a mental simulation process that incorporates the unreliability of the source and one's attitude toward ambiguity in the circumstances. A two-parameter model of this process is shown to be consistent with: Keynes' idea of the weight of evidence, the non-additivity of complementary probabilities, current psychological theories of risk, and Ellsberg's original paradox. The model is tested in four experiments at both the individual and group levels. In experiments 1-3, the model is shown to predict judgments quite well; in experiment 4, the inference model is shown to predict choices between gambles. The results and model are then discussed with respect to the importance of ambiguity in assessing perceived uncertainty; the use of cognitive strategies in judgments under ambiguity; the role of ambiguity in risky choice; and extensions of the model. (Author)

In this thesis, we present two approaches to a rigorous mathematical and algorithmic foundation of quantitative and statistical inference in constraint-based natural language processing. The first approach, called quantitative constraint logic programming, is conceptualized in a clear logical framework, and presents a sound and complete system of quantitative inference for definite clauses annotated with subjective weights. This approach combines a rigorous formal semantics for quantitative inference based on subjective weights with efficient weight-based pruning for constraint-based systems. The second approach, called probabilistic constraint logic programming, introduces a log-linear probability distribution on the proof trees of a constraint logic program and an algorithm for statistical inference of the parameters and properties of such probability models from incomplete, i.e., unparsed data. The possibility of defining arbitrary properties of proof trees as properties of the log-linear probability model and efficiently estimating appropriate parameter values for them permits the probabilistic modeling of arbitrary context-dependencies in constraint logic programs. The usefulness of these ideas is evaluated empirically in a small-scale experiment on finding the correct parses of a constraint-based grammar. In addition, we address the problem of computational intractability of the calculation of expectations in the inference task and present various techniques to approximately solve this task. Moreover, we present an approximate heuristic technique for searching for the most probable analysis in probabilistic constraint logic programs.

We identify various situations in probabilistic intelligent systems in which conditionals (rules) as mathematical entities as well as their conditional logic operations are needed. In discussing Bayesian updating procedure and belief function construction, we provide a new method for modeling if...then rules as Boolean elements, and yet, compatible with conditional probability quantifications.

This report describes how the Dirac algebra of quantum mechanics provides for a robust and self-consistent approach to probabilistic inference system modeling and processing. We call such systems Dirac networks and demonstrate how their use: (1) allows an efficient algebraic encoding of the probabilities and distributions for all possible combinations of truth values for the logical variable in an inference system; (2) employs unitary - rotation, time evolution, and translation operators to model influences upon system variable probabilities and their distributions; (3) guarantees system normalization; (4) admits unambiguously defined linear, as well as cyclic, cause and effect relationships; (5) enables the use of the von Neumann entropy as an informational uncertainty measure; and (6) allows for a variety of 'measurement' operators useful for quantifying probabilistic inferences. Dirac networks should have utility in such diverse application areas as data fusion and analysis, dynamic resource allocation, qualitative analysis of complex systems, automated medical diagnostics, and interactive/collaborative decision processes. The approach is illustrated by developing and applying simple Dirac networks to the following representative problems: (a) cruise missile - target allocation decision aiding; (b) genetic disease carrier identification using ancestral evidential information; (c) combat system control methodology trade-off analysis; (d) finding rotational symmetries in a digital image; and (e) fusing observational error profiles. Optical device implementations of several Dirac network components are also briefly discussed.

Models of complex systems are often formalized as sequential software simulators: computationally intensive programs that iteratively build up probable system configurations given parameters and initial conditions. These simulators enable modelers to capture effects that are difficult to characterize analytically or summarize statistically. However, in many real-world applications, these simulations need to be inverted to match the observed data. This typically requires the custom design, derivation and implementation of sophisticated inversion algorithms. Here we give a framework for inverting a broad class of complex software simulators via probabilistic programming and automatic inference, using under 20 lines of probabilistic code. Our approach is based on a formulation of inversion as approximate inference in a simple sequential probabilistic model. We implement four inference strategies, including Metropolis-Hastings, a sequentialized Metropolis-Hastings scheme, and a particle Markov chain Monte Carlo scheme, requiring 4 or fewer lines of probabilistic code each. We demonstrate our framework by applying it to invert a real geological software simulator from the oil and gas industry.

The properties of the normal distribution under linear transformation, as well the easy way to compute the covariance matrix of marginals and conditionals, offer a unique opportunity to get an insight about several aspects of uncertainties in measurements. The way to build the overall covariance matrix in a few, but conceptually relevant cases is illustrated: several observations made with (possibly) different instruments measuring the same quantity; effect of systematics (although limited to offset, in order to stick to linear models) on the determination of the 'true value', as well in the prediction of future observations; correlations which arise when different quantities are measured with the same instrument affected by an offset uncertainty; inferences and predictions based on averages; inference about constrained values; fits under some assumptions (linear models with known standard deviations). Many numerical examples are provided, exploiting the ability of the R language to handle large matrices and to produce high quality plots. Some of the results are framed in the general problem of 'propagation of evidence', crucial in analyzing graphical models of knowledge.

Probabilistic Logic Programming (PLP), exemplified by Sato and Kameya's PRISM, Poole's ICL, Raedt et al's ProbLog and Vennekens et al's LPAD, is aimed at combining statistical and logical knowledge representation and inference. A key characteristic of PLP frameworks is that they are conservative extensions to non-probabilistic logic programs which have been widely used for knowledge representation. PLP frameworks extend traditional logic programming semantics to a distribution semantics, where the semantics of a probabilistic logic program is given in terms of a distribution over possible models of the program. However, the inference techniques used in these works rely on enumerating sets of explanations for a query answer. Consequently, these languages permit very limited use of random variables with continuous distributions. In this paper, we present a symbolic inference procedure that uses constraints and represents sets of explanations without enumeration. This permits us to reason over PLPs with Gaussian or Gamma-distributed random variables (in addition to discrete-valued random variables) and linear equality constraints over reals. We develop the inference procedure in the context of PRISM; however the procedure's core ideas can be easily applied to other PLP languages as well. An interesting aspect of our inference procedure is that PRISM's query evaluation process becomes a special case in the absence of any continuous random variables in the program. The symbolic inference procedure enables us to reason over complex probabilistic models such as Kalman filters and a large subclass of Hybrid Bayesian networks that were hitherto not possible in PLP frameworks. (To appear in Theory and Practice of Logic Programming).

ChIP-seq, which combines chromatin immunoprecipitation with massively parallel short-read sequencing, can profile in vivo genome-wide transcription factor-DNA association with higher sensitivity, specificity and spatial resolution than ChIP-chip. While it presents new opportunities for research, ChIP-seq poses new challenges for statistical analysis that derive from the complexity of the biological systems characterized and the variability and biases in its digital sequence data. We propose a method called PICS (Probabilistic Inference for ChIP-seq) for extracting information from ChIP-seq aligned-read data in order to identify regions bound by transcription factors. PICS identifies enriched regions by modeling local concentrations of directional reads, and uses DNA fragment length prior information to discriminate closely adjacent binding events via a Bayesian hierarchical t-mixture model. Its per-event fragment length estimates also allow it to remove from analysis regions that have atypical lengths. PICS uses pre-calculated, whole-genome read mappability profiles and a truncated t-distribution to adjust binding event models for reads that are missing due to local genome repetitiveness. It estimates uncertainties in model parameters that can be used to define confidence regions on binding event locations and to filter estimates. Finally, PICS calculates a per-event enrichment score relative to a control sample, and can use a control sample to estimate a false discovery rate. We compared PICS to the alternative methods MACS, QuEST, and CisGenome, using published GABP and FOXA1 data sets from human cell lines, and found that PICS' predicted binding sites were more consistent with computationally predicted binding motifs.

Reports first-year results of project, The Use of Protocol Analysis and Process Tracing Techniques to Investigate Probabilistic Inference. Research indicates that the most recently presented information is given more attention in situations that require the integration of information about expectancies with uncertain information about what is happening at present. In addition, subjects have difficulty distinguishing two types of conditional probability information, the reliability p(evidence/hypothesis) and the probability that the hypothesis is true if the evidence is observed, p(hypothesis/evidence).

There are two profoundly different (though not exclusive) approaches to uncertain inference. According to one, uncertain inference leads from one distribution of (non-extreme) uncertainties among those propositions. According to the other, uncertain inference is like deductive inference in that the conclusion is detached from the premises (the evidence) and accepted as practically certain; it differs in being non-monotonic: and augmentation of the premises can lead to the withdrawal of conclusions already accepted. We show here, first, that probabilistic inference is what both traditional inductive logic (ampliative inference) and non-monotonic reasoning are designed to capture, third, that acceptance is legitimate and desirable, fourth, that statistical testing provides a model of probabilistic acceptance, and fifth, that a generalization of this model makes sense in AI.

There are two profoundly different (though not exclusive) approaches to uncertain inference. According to one, uncertain inference leads from one distribution of (non-extreme) uncertainties among those propositions. According to the other, uncertain inference is like deductive inference in that the conclusion is detached from the premises (the evidence) and accepted as practically certain; it differs in being non-monotonic: and augmentation of the premises can lead to the withdrawal of conclusions already accepted. We show here, first, that probabilistic inference is what both traditional inductive logic (ampliative inference) and non-monotonic reasoning are designed to capture, third, that acceptance is legitimate and desirable, fourth, that statistical testing provides a model of probabilistic acceptance, and fifth, that a generalization of this model makes sense in AI.

Information geometric techniques and inductive inference methods hold great promise for solving computational problems of interest in classical and quantum physics, especially with regard to complexity characterization of dynamical systems in terms of their probabilistic description on curved statistical manifolds. In this article, we investigate the possibility of describing the macroscopic behavior of complex systems in terms of the underlying statistical structure of their microscopic degrees of freedom by use of statistical inductive inference and information geometry. We review the Maximum Relative Entropy (MrE) formalism and the theoretical structure of the information geometrodynamical approach to chaos (IGAC) on statistical manifolds. Special focus is devoted to the description of the roles played by the sectional curvature, the Jacobi field intensity and the information geometrodynamical entropy (IGE). These quantities serve as powerful information geometric complexity measures of information-constrained dynamics associated with arbitrary chaotic and regular systems defined on the statistical manifold. Finally, the application of such information geometric techniques to several theoretical models are presented.

The abundance of data produced daily from large variety of sources has boosted the need of novel approaches on causal inference analysis from observational data. Observational data often contain noisy or missing entries. Moreover, causal inference studies may require unobserved high-level information which needs to be inferred from other observed attributes. In such cases, inaccuracies of the applied inference methods will result in noisy outputs. In this study, we propose a novel approach for causal inference when one or more key variables are noisy. Our method utilizes the knowledge about the uncertainty of the real values of key variables in order to reduce the bias induced by noisy measurements. We evaluate our approach in comparison with existing methods both on simulated and real scenarios and we demonstrate that our method reduces the bias and avoids false causal inference conclusions in most cases.

We propose a new class of quantum computing algorithms which generalize many standard ones. The goal of our algorithms is to estimate probability distributions. Such estimates are useful in, for example, applications of Decision Theory and Artificial Intelligence, where inferences are made based on uncertain knowledge. The class of algorithms that we propose is based on a construction method that generalizes a Fredkin-Toffoli (F-T) construction method used in the field of classical reversible computing. F-T showed how, given any binary deterministic circuit, one can construct another binary deterministic circuit which does the same calculations in a reversible manner. We show how, given any classical stochastic network (classical Bayesian net), one can construct a quantum network (quantum Bayesian net). By running this quantum Bayesian net on a quantum computer, one can calculate any conditional probability that one would be interested in calculating for the original classical Bayesian net. Thus, we generalize the F-T construction method so that it can be applied to any classical stochastic circuit, not just binary deterministic ones. We also show that, in certain situations, our class of algorithms can be combined with Grover's algorithm to great advantage.

In this work we present a flexible, probabilistic and reference-free method of error correction for high throughput DNA sequencing data. The key is to exploit the high coverage of sequencing data and model short sequence outputs as independent realizations of a Hidden Markov Model (HMM). We pose the problem of error correction of reads as one of maximum likelihood sequence detection over this HMM. While time and memory considerations rule out an implementation of the optimal Baum-Welch algorithm (for parameter estimation) and the optimal Viterbi algorithm (for error correction), we propose low-complexity approximate versions of both. Specifically, we propose an approximate Viterbi and a sequential decoding based algorithm for the error correction. Our results show that when compared with Reptile, a state-of-the-art error correction method, our methods consistently achieve superior performances on both simulated and real data sets.

The problem of optimal motion planing and control is fundamental in robotics. However, this problem is intractable for continuous-time stochastic systems in general and the solution is difficult to approximate if non-instantaneous nonlinear performance indices are present. In this work, we provide an efficient algorithm, PIPC (Probabilistic Inference for Planning and Control), that yields approximately optimal policies with arbitrary higher-order nonlinear performance indices. Using probabilistic inference and a Gaussian process representation of trajectories, PIPC exploits the underlying sparsity of the problem such that its complexity scales linearly in the number of nonlinear factors. We demonstrate the capabilities of our algorithm in a receding horizon setting with multiple systems in simulation.

We present a hierarchical probabilistic model for improving geometric stellar distance estimates using color--magnitude information. This is achieved with a data driven model of the color--magnitude diagram, not relying on stellar models but instead on the relative abundances of stars in color--magnitude cells, which are inferred from very noisy magnitudes and parallaxes. While the resulting noise-deconvolved color--magnitude diagram can be useful for a range of applications, we focus on deriving improved stellar distance estimates relying on both parallax and photometric information. We demonstrate the efficiency of this approach on the 1.4 million stars of the Gaia TGAS sample that also have APASS magnitudes. Our hierarchical model has 4~million parameters in total, most of which are marginalized out numerically or analytically. We find that distance estimates are significantly improved for the noisiest parallaxes and densest regions of the color--magnitude diagram. In particular, the average distance signal-to-noise ratio and uncertainty improve by 19~percent and 36~percent, respectively, with 8~percent of the objects improving in SNR by a factor greater than 2. This computationally efficient approach fully accounts for both parallax and photometric noise, and is a first step towards a full hierarchical probabilistic model of the Gaia data.

This paper addresses two main challenges facing systems neuroscience today: understanding the nature and function of a) cortical feedback between sensory areas and b) correlated variability. Starting from the old idea of perception as probabilistic inference, we show how to use knowledge of the psychophysical task to make easily testable predictions for the impact that feedback signals have on early sensory representations. Applying our framework to the well-studied two-alternative forced choice task paradigm, we can explain multiple empirical findings that have been hard to account for by the traditional feedforward model of sensory processing, including the task-dependence of neural response correlations, and the diverging time courses of choice probabilities and psychophysical kernels. Our model makes a number of new predictions and, importantly, characterizes a component of correlated variability that represents task-related information rather than performance-degrading noise. It also demonstrates a normative way to integrate sensory and cognitive components into physiologically testable mathematical models of perceptual decision-making.

Ambiguity results from having limited knowledge of the process that generates outcomes. It is argued that many real-world processes are perceived to be ambigious; moreover, as Ellsberg demonstrated, this poses problems for theories of probability operationalized via choices amongst gambles. A descriptive model of how people make judgments under ambiguity is proposed. The model assumes an anchoring-and-adjustment process in which an initial estimate provides the anchor, and adjustments are made for what might be. The latter is modeled as the result of a mental simulation process where the size of the simulation is a function of the amount of ambiguity, and differential weighting of imagined probabilities reflects one's attitude toward ambiguity. A two-parameter model of this process is shown to be consistent with: Ellsberg's original paradox, the non-additivity of complementary probabilities, current psycho-loical theories of risk, and Keynes' idea of the weight of evidence. The model is tested in four experiments involving boht individual and group analyses. In experiments 1 and 2, the model is shown to predict judgments quite well; in experiment 3, the inference model is shown to predict choices between gambles; experiment 4 shows how buying and selling prices for insurance are systematically influenced by one's attitude toward ambiguity.

This article is from PLoS Computational Biology , volume 10 . Abstract Humans have been shown to combine noisy sensory information with previous experience (priors), in qualitative and sometimes quantitative agreement with the statistically-optimal predictions of Bayesian integration. However, when the prior distribution becomes more complex than a simple Gaussian, such as skewed or bimodal, training takes much longer and performance appears suboptimal. It is unclear whether such suboptimality arises from an imprecise internal representation of the complex prior, or from additional constraints in performing probabilistic computations on complex distributions, even when accurately represented. Here we probe the sources of suboptimality in probabilistic inference using a novel estimation task in which subjects are exposed to an explicitly provided distribution, thereby removing the need to remember the prior. Subjects had to estimate the location of a target given a noisy cue and a visual representation of the prior probability density over locations, which changed on each trial. Different classes of priors were examined (Gaussian, unimodal, bimodal). Subjects' performance was in qualitative agreement with the predictions of Bayesian Decision Theory although generally suboptimal. The degree of suboptimality was modulated by statistical features of the priors but was largely independent of the class of the prior and level of noise in the cue, suggesting that suboptimality in dealing with complex statistical features, such as bimodality, may be due to a problem of acquiring the priors rather than computing with them. We performed a factorial model comparison across a large set of Bayesian observer models to identify additional sources of noise and suboptimality. Our analysis rejects several models of stochastic behavior, including probability matching and sample-averaging strategies. Instead we show that subjects' response variability was mainly driven by a combination of a noisy estimation of the parameters of the priors, and by variability in the decision process, which we represent as a noisy or stochastic posterior.

The development of statistical methods for valid and efficient probabilistic inference without prior distributions has a long history. Fisher's fiducial inference is perhaps the most famous of these attempts. We argue that, despite its seemingly prior-free formulation, fiducial and its various extensions are not prior-free and, therefore, do not meet the requirements for prior-free probabilistic inference. In contrast, the inferential model (IM) framework is genuinely prior-free and is shown to be a promising new method for generating both valid and efficient probabilistic inference. With a brief introduction to the two fundamental principles, namely, the validity and efficiency principles, the three-step construction of the basic IM framework is discussed in the context of the validity principle. Efficient IM methods, based on conditioning and marginalization are illustrated with two benchmark examples, namely, the bivariate normal with unknown correlation coefficient and the Behrens--Fisher problem.

We introduce a new approach to solving path-finding problems under uncertainty by representing them as probabilistic models and applying domain-independent inference algorithms to the models. This approach separates problem representation from the inference algorithm and provides a framework for efficient learning of path-finding policies. We evaluate the new approach on the Canadian Traveler Problem, which we formulate as a probabilistic model, and show how probabilistic inference allows high performance stochastic policies to be obtained for this problem.

Probabilistic Logic Programming (PLP) languages enable programmers to specify systems that combine logical models with statistical knowledge. The inference problem, to determine the probability of query answers in PLP, is intractable in general, thereby motivating the need for approximate techniques. In this paper, we present a technique for approximate inference of conditional probabilities for PLP queries. It is an Adaptive Markov Chain Monte Carlo (MCMC) technique, where the distribution from which samples are drawn is modified as the Markov Chain is explored. In particular, the distribution is progressively modified to increase the likelihood that a generated sample is consistent with evidence. In our context, each sample is uniquely characterized by the outcomes of a set of random variables. Inspired by reinforcement learning, our technique propagates rewards to random variable/outcome pairs used in a sample based on whether the sample was consistent or not. The cumulative rewards of each outcome is used to derive a new "adapted distribution" for each random variable. For a sequence of samples, the distributions are progressively adapted after each sample. For a query with "Markovian evaluation structure", we show that the adapted distribution of samples converges to the query's conditional probability distribution. For Markovian queries, we present a modified adaptation process that can be used in adaptive MCMC as well as adaptive independent sampling. We empirically evaluate the effectiveness of the adaptive sampling methods for queries with and without Markovian evaluation structure.

When dealing with incomplete data in statistical learning, or incomplete observations in probabilistic inference, one needs to distinguish the fact that a certain event is observed from the fact that the observed event has happened. Since the modeling and computational complexities entailed by maintaining this proper distinction are often prohibitive, one asks for conditions under which it can be safely ignored. Such conditions are given by the missing at random (mar) and coarsened at random (car) assumptions. In this paper we provide an in-depth analysis of several questions relating to mar/car assumptions. Main purpose of our study is to provide criteria by which one may evaluate whether a car assumption is reasonable for a particular data collecting or observational process. This question is complicated by the fact that several distinct versions of mar/car assumptions exist. We therefore first provide an overview over these different versions, in which we highlight the distinction between distributional and coarsening variable induced versions. We show that distributional versions are less restrictive and sufficient for most applications. We then address from two different perspectives the question of when the mar/car assumption is warranted. First we provide a static analysis that characterizes the admissibility of the car assumption in terms of the support structure of the joint probability distribution of complete data and incomplete observations. Here we obtain an equivalence characterization that improves and extends a recent result by Grunwald and Halpern. We then turn to a procedural analysis that characterizes the admissibility of the car assumption in terms of procedural models for the actual data (or observation) generating process. The main result of this analysis is that the stronger coarsened completely at random (ccar) condition is arguably the most reasonable assumption, as it alone corresponds to data coarsening procedures that satisfy a natural robustness property.

When dealing with incomplete data in statistical learning, or incomplete observations in probabilistic inference, one needs to distinguish the fact that a certain event is observed from the fact that the observed event has happened. Since the modeling and computational complexities entailed by maintaining this proper distinction are often prohibitive, one asks for conditions under which it can be safely ignored. Such conditions are given by the missing at random (mar) and coarsened at random (car) assumptions. In this paper we provide an in-depth analysis of several questions relating to mar/car assumptions. Main purpose of our study is to provide criteria by which one may evaluate whether a car assumption is reasonable for a particular data collecting or observational process. This question is complicated by the fact that several distinct versions of mar/car assumptions exist. We therefore first provide an overview over these different versions, in which we highlight the distinction between distributional and coarsening variable induced versions. We show that distributional versions are less restrictive and sufficient for most applications. We then address from two different perspectives the question of when the mar/car assumption is warranted. First we provide a static analysis that characterizes the admissibility of the car assumption in terms of the support structure of the joint probability distribution of complete data and incomplete observations. Here we obtain an equivalence characterization that improves and extends a recent result by Grunwald and Halpern. We then turn to a procedural analysis that characterizes the admissibility of the car assumption in terms of procedural models for the actual data (or observation) generating process. The main result of this analysis is that the stronger coarsened completely at random (ccar) condition is arguably the most reasonable assumption, as it alone corresponds to data coarsening procedures that satisfy a natural robustness property.

Many Artificial Intelligence (AI) tasks, such as natural language processing, commonsense reasoning and vision, could be naturally modeled by a language and associated inference engine using both relational (first-order) predicates and probabilistic information. While logic has been the basis for much AI development and is a powerful framework for using relational predicates, its lack of representation for probabilistic knowledge severely limits its application to many tasks. Graphical models and Machine Learning, on the other hand, can capture much of probabilistic reasoning but lack convenient means for using relational predicates. In the last fifteen years, many frameworks have been proposed for merging those two approaches but have mainly been probabilistic logic languages resorting to propositionalization of relational predicates (and, as a consequence, ordinary graphical models inference). This has the severe disadvantage of ignoring the relational structure of the model and potentially causing exponential blowups in inference time. I will talk about my work in integrating logic and probabilistic inference in a more seamless way. This includes Lifted First-Order Probabilistic Inference, a way of performing inference directly on first-order representation, without propositionalization, and work on DBLOG (Dynamic Bayesian Logic), an extension of BLOG (Bayesian Logic, by Milch and Russell) for temporal models such as data association and activity recognition. I will conclude with what I see as important future directions in this field. ©2008 Microsoft Corporation. All rights reserved.

Many Artificial Intelligence (AI) tasks, such as natural language processing, commonsense reasoning and vision, could be naturally modeled by a language and associated inference engine using both relational (first-order) predicates and probabilistic information. While logic has been the basis for much AI development and is a powerful framework for using relational predicates, its lack of representation for probabilistic knowledge severely limits its application to many tasks. Graphical models and Machine Learning, on the other hand, can capture much of probabilistic reasoning but lack convenient means for using relational predicates. In the last fifteen years, many frameworks have been proposed for merging those two approaches but have mainly been probabilistic logic languages resorting to propositionalization of relational predicates (and, as a consequence, ordinary graphical models inference). This has the severe disadvantage of ignoring the relational structure of the model and potentially causing exponential blowups in inference time. I will talk about my work in integrating logic and probabilistic inference in a more seamless way. This includes Lifted First-Order Probabilistic Inference, a way of performing inference directly on first-order representation, without propositionalization, and work on DBLOG (Dynamic Bayesian Logic), an extension of BLOG (Bayesian Logic, by Milch and Russell) for temporal models such as data association and activity recognition. I will conclude with what I see as important future directions in this field. ©2008 Microsoft Corporation. All rights reserved.

The promise of lifted probabilistic inference is to carry out probabilistic inference in a relational probabilistic model without needing to reason about each individual separately (grounding out the representation) by treating the undistinguished individuals as a block. Current exact methods still need to ground out in some cases, typically because the representation of the intermediate results is not closed under the lifted operations. We set out to answer the question as to whether there is some fundamental reason why lifted algorithms would need to ground out undifferentiated individuals. We have two main results: (1) We completely characterize the cases where grounding is polynomial in a population size, and show how we can do lifted inference in time polynomial in the logarithm of the population size for these cases. (2) For the case of no-argument and single-argument parametrized random variables where the grounding is not polynomial in a population size, we present lifted inference which is polynomial in the population size whereas grounding is exponential. Neither of these cases requires reasoning separately about the individuals that are not explicitly mentioned.

Exchangeability is a central notion in statistics and probability theory. The assumption that an infinite sequence of data points is exchangeable is at the core of Bayesian statistics. However, finite exchangeability as a statistical property that renders probabilistic inference tractable is less well-understood. We develop a theory of finite exchangeability and its relation to tractable probabilistic inference. The theory is complementary to that of independence and conditional independence. We show that tractable inference in probabilistic models with high treewidth and millions of variables can be understood using the notion of finite (partial) exchangeability. We also show that existing lifted inference algorithms implicitly utilize a combination of conditional independence and partial exchangeability.

Twitter provides an open and rich source of data for studying human behaviour at scale and is widely used in social and network sciences. However, a major criticism of Twitter data is that demographic information is largely absent. Enhancing Twitter data with user ages would advance our ability to study social network structures, information flows and the spread of contagions. Approaches toward age detection of Twitter users typically focus on specific properties of tweets, e.g., linguistic features, which are language dependent. In this paper, we devise a language-independent methodology for determining the age of Twitter users from data that is native to the Twitter ecosystem. The key idea is to use a Bayesian framework to generalise ground-truth age information from a few Twitter users to the entire network based on what/whom they follow. Our approach scales to inferring the age of 700 million Twitter accounts with high accuracy.