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 ofbenchmark 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.

First we demonstrate stiucture learning on a toy problem.

If we know PX and PY X, we can calculate this explicitly.

Predicting the document's sentiment would allow matching

We are at the beginning of the multicore era. Computers will have increasingly many cores (processors), but there is still no good programming framework for these architectures, and thus no simple and unified way for machine learning to take advantage of the potential speed up. In this paper, we develop a broadly applicable parallelprogramming method, one that is easily applied to many different learning algorithms. Our work is in distinct contrast to the tradition in machine learning of designing (often ingenious) ways to speed up a single algorithm at a time. Specifically, we show that algorithms that fit the Statistical Query model [15] can be written in a certain "summation form," which allows them to be easily parallelized onmulticore computers. We adapt Google's map-reduce [7] paradigm to demonstrate this parallel speed up technique on a variety of learning algorithms including locally weighted linear regression (LWLR), k-means, logistic regression (LR),naive Bayes (NB), SVM, ICA, PCA, gaussian discriminant analysis (GDA), EM, and backpropagation (NN). Our experimental results show basically linear speedup with an increasing number of processors.

Many unsupervised learning problems can be expressed as a form of matrix factorization, reconstructingan observed data matrix as the product of two matrices of latent variables. A standard challenge in solving these problems is determining the dimensionality of the latent matrices.

Markov networks are commonly used in a wide variety of applications, ranging from computer vision, to natural language, to computational biology. In most current applications, even those that rely heavily on learned models, the structure of the Markov network is constructed by hand, due to the lack of effective algorithms forlearning Markov network structure from data. In this paper, we provide a computationally efficient method for learning Markov network structure from data.

This paper proposes a new approach to model-based clustering under prior knowledge.

We rigorously establish a close relationship between message passing algorithms and models of neurodynamics by showing that the equations of a continuous Hopfield networkcan be derived from the equations of belief propagation on a binary Markov random field. As Hopfield networks are equipped with a Lyapunov function, convergenceis guaranteed. As a consequence, in the limit of many weak connections perneuron, Hopfield networks exactly implement a continuous-time variant of belief propagation starting from message initialisations that prevent from running into convergence problems. Our results lead to a better understanding of the role of message passing algorithms in real biological neural networks.

We describe Hidden Semi-Markov Support Vector Machines (SHM SVMs), an extension of HM SVMs to semi-Markov chains. This allows us to predict segmentations ofsequences based on segment-based features measuring properties such as the length of the segment. We propose a novel technique to partition the problem into sub-problems. The independently obtained partial solutions can then be recombined in an efficient way, which allows us to solve label sequence learning problemswith several thousands of labeled sequences. We have tested our algorithm for predicting gene structures, an important problem in computational biology. Results on a well-known model organism illustrate the great potential of SHM SVMs in computational biology.