Images are ambiguous at each of many levels of a contextual hi(cid:173) erarchy. Nevertheless, the high-level interpretation of most scenes is unambiguous, as evidenced by the superior performance of hu(cid:173) mans. This observation argues for global vision models, such as de(cid:173) formable templates. Unfortunately, such models are computation(cid:173) ally intractable for unconstrained problems. We propose a composi(cid:173) tional model in which primitives are recursively composed, subject to syntactic restrictions, to form tree-structured objects and object groupings.

In previous work [6, 9, 10], we advanced a new technique for direct visual matching of images for the purposes of face recognition and image retrieval, using a probabilistic measure of similarity based primarily on a Bayesian (MAP) analysis of image differ(cid:173) ences, leading to a "dual" basis similar to eigenfaces [13]. The performance advantage of this probabilistic matching technique over standard Euclidean nearest-neighbor eigenface matching was recently demonstrated using results from DARPA's 1996 "FERET" face recognition competition, in which this probabilistic matching algorithm was found to be the top performer. We have further developed a simple method of replacing the costly com put ion of nonlinear (online) Bayesian similarity measures by the relatively inexpensive computation of linear (offline) subspace projections and simple (online) Euclidean norms, thus resulting in a significant computational speed-up for implementation with very large image databases as typically encountered in real-world applications.

We describe Maximum-Likelihood Continuity Mapping (MALCOM), an alternative to hidden Markov models (HMMs) for processing sequence data such as speech. While HMMs have a discrete "hidden" space con(cid:173) strained by a fixed finite-automaton architecture, MALCOM has a con(cid:173) tinuous hidden space-a continuity map-that is constrained only by a smoothness requirement on paths through the space. MALCOM fits into the same probabilistic framework for speech recognition as HMMs, but it represents a more realistic model of the speech production process. To evaluate the extent to which MALCOM captures speech production information, we generated continuous speech continuity maps for three speakers and used the paths through them to predict measured speech articulator data. The median correlation between the MALCOM paths obtained from only the speech acoustics and articulator measurements was 0.77 on an independent test set not used to train MALCOM or the predictor.

This survey paper presents a comprehensive analysis of crime prediction methodologies, exploring the various techniques and technologies utilized in this area. The paper covers the statistical methods, machine learning algorithms, and deep learning techniques employed to analyze crime data, while also examining their effectiveness and limitations. We propose a methodological taxonomy that classifies crime prediction algorithms into specific techniques. This taxonomy is structured into four tiers, including methodology category, methodology sub-category, methodology techniques, and methodology sub-techniques. Empirical and experimental evaluations are provided to rank the different techniques. The empirical evaluation assesses the crime prediction techniques based on four criteria, while the experimental evaluation ranks the algorithms that employ the same sub-technique, the different sub-techniques that employ the same technique, the different techniques that employ the same methodology sub-category, the different methodology sub-categories within the same category, and the different methodology categories. The combination of methodological taxonomy, empirical evaluations, and experimental comparisons allows for a nuanced and comprehensive understanding of crime prediction algorithms, aiding researchers in making informed decisions. Finally, the paper provides a glimpse into the future of crime prediction techniques, highlighting potential advancements and opportunities for further research in this field

Bayesian optimization is a widely used technique for optimizing black-box functions, with Expected Improvement (EI) being the most commonly utilized acquisition function in this domain. While EI is often viewed as distinct from other information-theoretic acquisition functions, such as entropy search (ES) and max-value entropy search (MES), our work reveals that EI can be considered a special case of MES when approached through variational inference (VI). In this context, we have developed the Variational Entropy Search (VES) methodology and the VES-Gamma algorithm, which adapts EI by incorporating principles from information-theoretic concepts. The efficacy of VES-Gamma is demonstrated across a variety of test functions and read datasets, highlighting its theoretical and practical utilities in Bayesian optimization scenarios.

The standard approach to Computational Learning Theory is usually formulated within the so-called frequentist approach to Statistics. Within this paradigm one is interested in constructing an estimator, based on a flnite sample, which possesses a small loss (generalization error). While many algorithms have been constructed and analyzed within this context, it is not clear how these approaches relate to standard optimality criteria within the frequentist framework. Two classic optimality criteria within the latter approach are the minimax and admissibility criteria, which charac- terize optimality of estimators in a rigorous and precise fashion [9]. Except in some special cases [12], it is not known whether any of the approaches used within the Learning community lead to optimality in either of the above senses of the word. On the other hand, it is known that under certain regularity conditions, Bayesian estimators lead to either minimax or admissible estimators, and thus to well-deflned optimality in the classical (frequentist) sense. In fact, it can be shown that Bayes estimators are essentially the only estimators which can achieve optimality in the above senses [9]. This optimality feature provides strong motivation for the study of Bayesian approaches in a frequentist setting.

Machine learning has reached a point where many probabilistic meth- ods can be understood as variations, extensions and combinations of a much smaller set of abstract themes, e.g., as different instances of the EM algorithm. This enables the systematic derivation of algorithms cus- tomized for different models. Here, we describe the AUTO BAYES sys- tem which takes a high-level statistical model specification, uses power- ful symbolic techniques based on schema-based program synthesis and computer algebra to derive an efficient specialized algorithm for learning that model, and generates executable code implementing that algorithm. This capability is far beyond that of code collections such as Matlab tool- boxes or even tools for model-independent optimization such as BUGS for Gibbs sampling: complex new algorithms can be generated with- out new programming, algorithms can be highly specialized and tightly crafted for the exact structure of the model and data, and efficient and commented code can be generated for different languages or systems. We describe a symbolic program synthesis system which works as a "statistical algorithm compiler:" it compiles a statistical model specification into a custom algorithm design and from that further down into a working program implementing the algorithm design.

In the analysis of natural images, Gaussian scale mixtures (GSM) have been used to account for the statistics of (cid:2)lter responses, and to inspire hi- erarchical cortical representational learning schemes. GSMs pose a crit- ical assignment problem, working out which (cid:2)lter responses were gen- erated by a common multiplicative factor. We present a new approach to solving this assignment problem through a probabilistic extension to the basic GSM, and show how to perform inference in the model using Gibbs sampling. We demonstrate the ef(cid:2)cacy of the approach on both synthetic and image data. Understanding the statistical structure of natural images is an important goal for visual neuroscience.

We present a computational Bayesian approach for Wiener diffusion models, which are prominent accounts of response time distributions in decision-making. We first develop a general closed-form analytic approximation to the response time distributions for one-dimensional diffusion processes, and derive the required Wiener diffusion as a special case. We use this result to undertake Bayesian modeling of benchmark data, using posterior sampling to draw inferences about the interesting psychological parameters. With the aid of the benchmark data, we show the Bayesian account has several advantages, including dealing naturally with the parameter variation needed to account for some key features of the data, and providing quantitative measures to guide decisions about model construction.

The goal of perception is to infer the hidden states in the hierarchical process by which sensory data are generated. Human behavior is consistent with the optimal statistical solution to this problem in many tasks, including cue combination and orientation detection. Understanding the neural mechanisms underlying this behavior is of particular importance, since probabilistic computations are notoriously challenging. Here we propose a simple mechanism for Bayesian inference which involves averaging over a few feature detection neurons which fire at a rate determined by their similarity to a sensory stimulus. This mechanism is based on a Monte Carlo method known as importance sampling, commonly used in computer science and statistics.