The Bayesian online change point detection (BOCPD) algorithm provides an efficient way to do exact inference when the parameters of an underlying model may suddenly change over time. BOCPD requires computation of the underlying model's posterior predictives, which can only be computed online in $O(1)$ time and memory for exponential family models. We develop variational approximations to the posterior on change point times (formulated as run lengths) for efficient inference when the underlying model is not in the exponential family, and does not have tractable posterior predictive distributions. In doing so, we develop improvements to online variational inference. We apply our methodology to a tracking problem using radar data with a signal-to-noise feature that is Rice distributed. We also develop a variational method for inferring the parameters of the (non-exponential family) Rice distribution.

It has long been recognised that statistical dependencies in neuronal activity need to be taken into account when decoding stimuli encoded in a neural population. Less studied, though equally pernicious, is the need to take account of dependencies between synaptic weights when decoding patterns previously encoded in an auto-associative memory. We show that activity-dependent learning generically produces such correlations, and failing to take them into account in the dynamics of memory retrieval leads to catastrophically poor recall. We derive optimal network dynamics for recall in the face of synaptic correlations caused by a range of synaptic plasticity rules. These dynamics involve well-studied circuit motifs, such as forms of feedback inhibition and experimentally observed dendritic nonlinearities. We therefore show how addressing the problem of synaptic correlations leads to a novel functional account of key biophysical features of the neural substrate.

We introduce a novel variational method that allows to approximately integrate out kernel hyperparameters, such as length-scales, in Gaussian process regression. This approach consists of a novel variant of the variational framework that has been recently developed for the Gaussian process latent variable model which additionally makes use of a standardised representation of the Gaussian process. We consider this technique for learning Mahalanobis distance metrics in a Gaussian process regression setting and provide experimental evaluations and comparisons with existing methods by considering datasets with high-dimensional inputs.

Infinite mixture models are commonly used for clustering. One can sample from the posterior of mixture assignments by Monte Carlo methods or find its maximum a posteriori solution by optimization. However, in some problems the posterior is diffuse and it is hard to interpret the sampled partitionings. In this paper, we introduce novel statistics based on block sizes for representing sample sets of partitionings and feature allocations. We develop an element-based definition of entropy to quantify segmentation among their elements. Then we propose a simple algorithm called entropy agglomeration (EA) to summarize and visualize this information. Experiments on various infinite mixture posteriors as well as a feature allocation dataset demonstrate that the proposed statistics are useful in practice.

We study optimal image encoding based on a generative approach with non-linear feature combinations and explicit position encoding. By far most approaches to unsupervised learning learning of visual features, such as sparse coding or ICA, account for translations by representing the same features at different positions. Some earlier models used a separate encoding of features and their positions to facilitate invariant data encoding and recognition. All probabilistic generative models with explicit position encoding have so far assumed a linear superposition of components to encode image patches. Here, we for the first time apply a model with non-linear feature superposition and explicit position encoding. By avoiding linear superpositions, the studied model represents a closer match to component occlusions which are ubiquitous in natural images. In order to account for occlusions, the non-linear model encodes patches qualitatively very different from linear models by using component representations separated into mask and feature parameters. We first investigated encodings learned by the model using artificial data with mutually occluding components. We find that the model extracts the components, and that it can correctly identify the occlusive components with the hidden variables of the model. On natural image patches, the model learns component masks and features for typical image components. By using reverse correlation, we estimate the receptive fields associated with the model's hidden units. We find many Gabor-like or globular receptive fields as well as fields sensitive to more complex structures. Our results show that probabilistic models that capture occlusions and invariances can be trained efficiently on image patches, and that the resulting encoding represents an alternative model for the neural encoding of images in the primary visual cortex.

In order to learn effective control policies for dynamical systems, policy search methods must be able to discover successful executions of the desired task. While random exploration can work well in simple domains, complex and high-dimensional tasks present a serious challenge, particularly when combined with high-dimensional policies that make parameter-space exploration infeasible. We present a method that uses trajectory optimization as a powerful exploration strategy that guides the policy search. A variational decomposition of a maximum likelihood policy objective allows us to use standard trajectory optimization algorithms such as differential dynamic programming, interleaved with standard supervised learning for the policy itself. We demonstrate that the resulting algorithm can outperform prior methods on two challenging locomotion tasks.

This paper presents four major results towards solving decentralized partially observable Markov decision problems (DecPOMDPs) culminating in an algorithm that outperforms all existing algorithms on all but one standard infinite-horizon benchmark problems. (1) We give an integer program that solves collaborative Bayesian games (CBGs). The program is notable because its linear relaxation is very often integral. (2) We show that a DecPOMDP with bounded belief can be converted to a POMDP (albeit with actions exponential in the number of beliefs). These actions correspond to strategies of a CBG. (3) We present a method to transform any DecPOMDP into a DecPOMDP with bounded beliefs (the number of beliefs is a free parameter) using optimal (not lossless) belief compression. (4) We show that the combination of these results opens the door for new classes of DecPOMDP algorithms based on previous POMDP algorithms. We choose one such algorithm, point-based valued iteration, and modify it to produce the first tractable value iteration method for DecPOMDPs which outperforms existing algorithms.

We present a maximum margin framework that clusters data using latent variables. Using latent representations enables our framework to model unobserved information embedded in the data. We implement our idea by large margin learning, and develop an alternating descent algorithm to effectively solve the resultant non-convex optimization problem. We instantiate our latent maximum margin clustering framework with tag-based video clustering tasks, where each video is represented by a latent tag model describing the presence or absence of video tags. Experimental results obtained on three standard datasets show that the proposed method outperforms non-latent maximum margin clustering as well as conventional clustering approaches.

Psychophysical experiments have demonstrated that the brain integrates information from multiple sensory cues in a near Bayesian optimal manner. The present study proposes a novel mechanism to achieve this. We consider two reciprocally connected networks, mimicking the integration of heading direction information between the dorsal medial superior temporal (MSTd) and the ventral intraparietal (VIP) areas. Each network serves as a local estimator and receives an independent cue, either the visual or the vestibular, as direct input for the external stimulus. We find that positive reciprocal interactions can improve the decoding accuracy of each individual network as if it implements Bayesian inference from two cues. Our model successfully explains the experimental finding that both MSTd and VIP achieve Bayesian multisensory integration, though each of them only receives a single cue as direct external input. Our result suggests that the brain may implement optimal information integration distributively at each local estimator through the reciprocal connections between cortical regions.

Today, with respect to the increasing growth of demand to get credit from the customers of banks and finance and credit institutions, using an effective and efficient method to decrease the risk of non-repayment of credit given is very necessary. Assessment of customers' credit is one of the most important and the most essential duties of banks and institutions, and if an error occurs in this field, it would leads to the great losses for banks and institutions. Thus, using the predicting computer systems has been significantly progressed in recent decades. The data that are provided to the credit institutions' managers help them to make a straight decision for giving the credit or not-giving it. In this paper, we will assess the customer credit through a combined classification using artificial neural networks, genetics algorithm and Bayesian probabilities simultaneously, and the results obtained from three methods mentioned above would be used to achieve an appropriate and final result. We use the K_folds cross validation test in order to assess the method and finally, we compare the proposed method with the methods such as Clustering-Launched Classification (CLC), Support Vector Machine (SVM) as well as GA SVM where the genetics algorithm has been used to improve them. Keywords-Data classification; Combined Clustring; Artificial Neural Networks; Genetics Algorithm; Bayyesian Probabilities.