Bayesian inference systems should be able to explain their reasoning to users, translating from numerical to natural language. Previous empirical work has investigated the correspondence between absolute probabilities and linguistic phrases. This study extends that work to the correspondence between changes in probabilities (updates) and relative probability phrases, such as "much more likely" or "a little less likely." Subjects selected such phrases to best describe numerical probability updates. We examined three hypotheses about the correspondence, and found the most descriptively accurate of these three to be that each such phrase corresponds to a fixed difference in probability (rather than fixed ratio of probabilities or of odds). The empirically derived phrase selection function uses eight phrases and achieved a 72% accuracy in correspondence with the subjects' actual usage.
This extended abstract presents a logic, called Lp, that is capable of representing and reasoning with a wide variety of both qualitative and quantitative statistical information. The advantage of this logical formalism is that it offers a declarative representation of statistical knowledge; knowledge represented in this manner can be used for a variety of reasoning tasks. The logic differs from previous work in probability logics in that it uses a probability distribution over the domain of discourse, whereas most previous work (e.g., Nilsson [2], Scott et al. [3], Gaifinan [4], Fagin et al. [5]) has investigated the attachment of probabilities to the sentences of the logic (also, see Halpern [6] and Bacchus [7] for further discussion of the differences). The logic Lp possesses some further important features. First, Lp is a superset of first order logic, hence it can represent ordinary logical assertions. This means that Lp provides a mechanism for integrating statistical information and reasoning about uncertainty into systems based solely on logic. Second, Lp possesses transparent semantics, based on sets and probabilities of those sets. Hence, knowledge represented in Lp can be understood in terms of the simple primative concepts of sets and probabilities. And finally, the there is a sound proof theory that has wide coverage (the proof theory is complete for certain classes of models). The proof theory captures a sufficient range of valid inferences to subsume most previous probabilistic uncertainty reasoning systems. For example, the linear constraints like those generated by Nilsson's probabilistic entailment [2] can be generated by the proof theory, and the Bayesian inference underlying belief nets [8] can be performed. In addition, the proof theory integrates quantitative and qualitative reasoning as well as statistical and logical reasoning. In the next section we briefly examine previous work in probability logics, comparing it to Lp. Then we present some of the varieties of statistical information that Lp is capable of expressing. After this we present, briefly, the syntax, semantics, and proof theory of the logic. We conclude with a few examples of knowledge representation and reasoning in Lp, pointing out the advantages of the declarative representation offered by Lp. We close with a brief discussion of probabilities as degrees of belief, indicating how such probabilities can be generated from statistical knowledge encoded in Lp. The reader who is interested in a more complete treatment should consult Bacchus [7].
We are interested in creating an automated or semi-automated system with the capability of taking a set of radar imagery, collection parameters and a priori map and other tactical data, and producing likely interpretations of the possible military situations given the available evidence. This paper is concerned with the problem of the interpretation and computation of certainty or belief in the conclusions reached by such a system.
In [12], Nilsson proposed the probabilistic logic in which the truth values of logical propositions are probability values between 0 and 1. It is applicable to any logical system for which the consistency of a finite set of propositions can be established. The probabilistic inference scheme reduces to the ordinary logical inference when the probabilities of all propositions are either 0 or 1. This logic has the same limitations of other probabilistic reasoning systems of the Bayesian approach. For common sense reasoning, consistency is not a very natural assumption. We have some well known examples: {Dick is a Quaker, Quakers are pacifists, Republicans are not pacifists, Dick is a Republican}and {Tweety is a bird, birds can fly, Tweety is a penguin}. In this paper, we shall propose some extensions of the probabilistic logic. In the second section, we shall consider the space of all interpretations, consistent or not. In terms of frames of discernment, the basic probability assignment (bpa) and belief function can be defined. Dempster's combination rule is applicable. This extension of probabilistic logic is called the evidential logic in [ 1]. For each proposition s, its belief function is represented by an interval [Spt(s), Pls(s)]. When all such intervals collapse to single points, the evidential logic reduces to probabilistic logic (in the generalized version of not necessarily consistent interpretations). Certainly, we get Nilsson's probabilistic logic by further restricting to consistent interpretations. In the third section, we shall give a probabilistic interpretation of probabilistic logic in terms of multi-dimensional random variables. This interpretation brings the probabilistic logic into the framework of probability theory. Let us consider a finite set S = {sl, s2, ..., Sn) of logical propositions. Each proposition may have true or false values; and may be considered as a random variable. We have a probability distribution for each proposition. The e-dimensional random variable (sl,..., Sn) may take values in the space of all interpretations of 2n binary vectors. We may compute absolute (marginal), conditional and joint probability distributions. It turns out that the permissible probabilistic interpretation vector of Nilsson [12] consists of the joint probabilities of S. Inconsistent interpretations will not appear, by setting their joint probabilities to be zeros. By summing appropriate joint probabilities, we get probabilities of individual propositions or subsets of propositions. Since the Bayes formula and other techniques are valid for e-dimensional random variables, the probabilistic logic is actually very close to the Bayesian inference schemes. In the last section, we shall consider a relaxation scheme for probabilistic logic. In this system, not only new evidences will update the belief measures of a collection of propositions, but also constraint satisfaction among these propositions in the relational network will revise these measures. This mechanism is similar to human reasoning which is an evaluative process converging to the most satisfactory result. The main idea arises from the consistent labeling problem in computer vision. This method is originally applied to scene analysis of line drawings. Later, it is applied to matching, constraint satisfaction and multi sensor fusion by several authors [8], [16] (and see references cited there). Recently, this method is used in knowledge aggregation by Landy and Hummel [9].
The fundamental elements of evidential reasoning problems are described, followed by a discussion of the structure of various types of problems. Bayesian inference networks and state space formalism are used as the tool for problem representation. A human-oriented decision making cycle for solving evidential reasoning problems is described and illustrated for a military situation assessment problem. The implementation of this cycle may serve as the basis for an expert system shell for evidential reasoning; i.e. a situation assessment processor.
This is a preliminary version of visual interpretation integrating multiple sensors in SUCCESSOR, an intelligent, model-based vision system. We pursue a thorough integration of hierarchical Bayesian inference with comprehensive physical representation of objects and their relations in a system for reasoning with geometry, surface materials and sensor models in machine vision. Bayesian inference provides a framework for accruing_ probabilities to rank order hypotheses.
Reinforcement learning methods are increasingly used to optimise dialogue policies from experience. Most current techniques are model-free: they directly estimate the utility of various actions, without explicit model of the interaction dynamics. In this paper, we investigate an alternative strategy grounded in model-based Bayesian reinforcement learning. Bayesian inference is used to maintain a posterior distribution over the model parameters, reflecting the model uncertainty. This parameter distribution is gradually refined as more data is collected and simultaneously used to plan the agent's actions. Within this learning framework, we carried out experiments with two alternative formalisations of the transition model, one encoded with standard multinomial distributions, and one structured with probabilistic rules. We demonstrate the potential of our approach with empirical results on a user simulator constructed from Wizard-of-Oz data in a human-robot interaction scenario. The results illustrate in particular the benefits of capturing prior domain knowledge with high-level rules.
Author co-citation studies employ factor analysis to reduce high-dimensional co-citation matrices to low-dimensional and possibly interpretable factors, but these studies do not use any information from the text bodies of publications. We hypothesise that term frequencies may yield useful information for scientometric analysis. In our work we ask if word features in combination with Bayesian analysis allow well-founded science mapping studies. This work goes back to the roots of Mosteller and Wallace's (1964) statistical text analysis using word frequency features and a Bayesian inference approach, tough with different goals. To answer our research question we (i) introduce a new data set on which the experiments are carried out, (ii) describe the Bayesian model employed for inference and (iii) present first results of the analysis.
A popular approach for large scale data annotation tasks is crowdsourcing, wherein each data point is labeled by multiple noisy annotators. We consider the problem of inferring ground truth from noisy ordinal labels obtained from multiple annotators of varying and unknown expertise levels. Annotation models for ordinal data have been proposed mostly as extensions of their binary/categorical counterparts and have received little attention in the crowdsourcing literature. We propose a new model for crowdsourced ordinal data that accounts for instance difficulty as well as annotator expertise, and derive a variational Bayesian inference algorithm for parameter estimation. We analyze the ordinal extensions of several state-of-the-art annotator models for binary/categorical labels and evaluate the performance of all the models on two real world datasets containing ordinal query-URL relevance scores, collected through Amazon's Mechanical Turk. Our results indicate that the proposed model performs better or as well as existing state-of-the-art methods and is more resistant to `spammy' annotators (i.e., annotators who assign labels randomly without actually looking at the instance) than popular baselines such as mean, median, and majority vote which do not account for annotator expertise.
A mean field variational Bayes approach to support vector machines (SVMs) using the latent variable representation on Polson & Scott (2012) is presented. This representation allows circumvention of many of the shortcomings associated with classical SVMs including automatic penalty parameter selection, the ability to handle dependent samples, missing data and variable selection. We demonstrate on simulated and real datasets that our approach is easily extendable to non-standard situations and outperforms the classical SVM approach whilst remaining computationally efficient.
In the internet era there has been an explosion in the amount of digital text information available, leading to difficulties of scale for traditional inference algorithms for topic models. Recent advances in stochastic variational inference algorithms for latent Dirichlet allocation (LDA) have made it feasible to learn topic models on large-scale corpora, but these methods do not currently take full advantage of the collapsed representation of the model. We propose a stochastic algorithm for collapsed variational Bayesian inference for LDA, which is simpler and more efficient than the state of the art method. We show connections between collapsed variational Bayesian inference and MAP estimation for LDA, and leverage these connections to prove convergence properties of the proposed algorithm. In experiments on large-scale text corpora, the algorithm was found to converge faster and often to a better solution than the previous method. Human-subject experiments also demonstrated that the method can learn coherent topics in seconds on small corpora, facilitating the use of topic models in interactive document analysis software.
Competition between a complex system's constituents and a corresponding reward mechanism based on it have profound influence on the functioning, stability, and evolution of the system. But determining the dominance hierarchy or ranking among the constituent parts from the strongest to the weakest -- essential in determining reward or penalty -- is almost always an ambiguous task due to the incomplete nature of competition networks. Here we introduce ``Natural Ranking," a desirably unambiguous ranking method applicable to a complete (full) competition network, and formulate an analytical model based on the Bayesian formula inferring the expected mean and error of the natural ranking of nodes from an incomplete network. We investigate its potential and uses in solving issues in ranking by applying to a real-world competition network of economic and social importance.
Latent Gaussian models (LGMs) are widely used in statistics and machine learning. Bayesian inference in non-conjugate LGMs is difficult due to intractable integrals involving the Gaussian prior and non-conjugate likelihoods. Algorithms based on variational Gaussian (VG) approximations are widely employed since they strike a favorable balance between accuracy, generality, speed, and ease of use. However, the structure of the optimization problems associated with these approximations remains poorly understood, and standard solvers take too long to converge. We derive a novel dual variational inference approach that exploits the convexity property of the VG approximations. We obtain an algorithm that solves a convex optimization problem, reduces the number of variational parameters, and converges much faster than previous methods. Using real-world data, we demonstrate these advantages on a variety of LGMs, including Gaussian process classification, and latent Gaussian Markov random fields.
One of the fundamental requirements for visual surveillance using non-overlapping camera networks is the correct labeling of tracked objects on each camera in a consistent way,in the sense that the captured tracklets, or observations in this paper, of the same object at different cameras should be assigned with the same label. In this paper, we formulate this task as a Bayesian inference problem and propose a distributed inference framework in which the posterior distribution of labeling variable corresponding to each observation, conditioned on all history appearance and spatio-temporal evidence made in the whole networks, is calculated based solely on local information processing on each camera and mutual information exchanging between neighboring cameras. In our framework, the number of objects presenting in the monitored region, i.e. the sampling space of labeling variables, does not need to be specified beforehand. Instead, it can be determined automatically on the fly. In addition, we make no assumption about the appearance distribution of a single object, but use similarity scores between appearance pairs, given by advanced object re-identification algorithm, as appearance likelihood for inference. This feature makes our method very flexible and competitive when observing condition undergoes large changes across camera views. To cope with the problem of missing detection, which is critical for distributed inference, we consider an enlarged neighborhood of each camera during inference and use a mixture model to describe the higher order spatio-temporal constraints. The robustness of the algorithm against missing detection is improved at the cost of slightly increased computation and communication burden at each camera node. Finally, we demonstrate the effectiveness of our method through experiments on an indoor Office Building dataset and an outdoor Campus Garden dataset.
Probabilistic programming allows specification of probabilistic models in a declarative manner. Recently, several new software systems and languages for probabilistic programming have been developed on the basis of newly developed and improved methods for approximate inference in probabilistic models. In this contribution a probabilistic model for an idealized dark matter localization problem is described. We first derive the probabilistic model for the inference of dark matter locations and masses, and then show how this model can be implemented using BUGS and Infer.NET, two software systems for probabilistic programming. Finally, the different capabilities of both systems are discussed. The presented dark matter model includes mainly non-conjugate factors, thus, it is difficult to implement this model with Infer.NET.
Typical blur from camera shake often deviates from the standard uniform convolutional script, in part because of problematic rotations which create greater blurring away from some unknown center point. Consequently, successful blind deconvolution requires the estimation of a spatially-varying or non-uniform blur operator. Using ideas from Bayesian inference and convex analysis, this paper derives a non-uniform blind deblurring algorithm with several desirable, yet previously-unexplored attributes. The underlying objective function includes a spatially adaptive penalty which couples the latent sharp image, non-uniform blur operator, and noise level together. This coupling allows the penalty to automatically adjust its shape based on the estimated degree of local blur and image structure such that regions with large blur or few prominent edges are discounted. Remaining regions with modest blur and revealing edges therefore dominate the overall estimation process without explicitly incorporating structure-selection heuristics. The algorithm can be implemented using a majorization-minimization strategy that is virtually parameter free. Detailed theoretical analysis and empirical validation on real images serve to validate the proposed method.
In modeling multivariate time series, it is important to allow time-varying smoothness in the mean and covariance process. In particular, there may be certain time intervals exhibiting rapid changes and others in which changes are slow. If such time-varying smoothness is not accounted for, one can obtain misleading inferences and predictions, with over-smoothing across erratic time intervals and under-smoothing across times exhibiting slow variation. This can lead to mis-calibration of predictive intervals, which can be substantially too narrow or wide depending on the time. We propose a locally adaptive factor process for characterizing multivariate mean-covariance changes in continuous time, allowing locally varying smoothness in both the mean and covariance matrix. This process is constructed utilizing latent dictionary functions evolving in time through nested Gaussian processes and linearly related to the observed data with a sparse mapping. Using a differential equation representation, we bypass usual computational bottlenecks in obtaining MCMC and online algorithms for approximate Bayesian inference. The performance is assessed in simulations and illustrated in a financial application.
We review three algorithms for Latent Dirichlet Allocation (LDA). Two of them are variational inference algorithms: Variational Bayesian inference and Online Variational Bayesian inference and one is Markov Chain Monte Carlo (MCMC) algorithm -- Collapsed Gibbs sampling. We compare their time complexity and performance. We find that online variational Bayesian inference is the fastest algorithm and still returns reasonably good results.
We consider the problem of learning by demonstration from agents acting in unknown stochastic Markov environments or games. Our aim is to estimate agent preferences in order to construct improved policies for the same task that the agents are trying to solve. To do so, we extend previous probabilistic approaches for inverse reinforcement learning in known MDPs to the case of unknown dynamics or opponents. We do this by deriving two simplified probabilistic models of the demonstrator's policy and utility. For tractability, we use maximum a posteriori estimation rather than full Bayesian inference. Under a flat prior, this results in a convex optimisation problem. We find that the resulting algorithms are highly competitive against a variety of other methods for inverse reinforcement learning that do have knowledge of the dynamics.
We propose a new data-augmentation strategy for fully Bayesian inference in models with binomial likelihoods. The approach appeals to a new class of Polya-Gamma distributions, which are constructed in detail. A variety of examples are presented to show the versatility of the method, including logistic regression, negative binomial regression, nonlinear mixed-effects models, and spatial models for count data. In each case, our data-augmentation strategy leads to simple, effective methods for posterior inference that: (1) circumvent the need for analytic approximations, numerical integration, or Metropolis-Hastings; and (2) outperform other known data-augmentation strategies, both in ease of use and in computational efficiency. All methods, including an efficient sampler for the Polya-Gamma distribution, are implemented in the R package BayesLogit. In the technical supplement appended to the end of the paper, we provide further details regarding the generation of Polya-Gamma random variables; the empirical benchmarks reported in the main manuscript; and the extension of the basic data-augmentation framework to contingency tables and multinomial outcomes.