We study the synthesis of neural coding, selective attention and perceptual decision making. A hierarchical neural architecture is proposed, which implements Bayesian integration of noisy sensory input and topdown attentional priors, leading to sound perceptual discrimination. The model offers an explicit explanation for the experimentally observed modulation that prior information in one stimulus feature (location) can have on an independent feature (orientation). The network's intermediate levels of representation instantiate known physiological properties of visual cortical neurons. The model also illustrates a possible reconciliation of cortical and neuromodulatory representations of uncertainty.

Linear Discriminant Analysis (LDA) is a well-known scheme for feature extraction and dimension reduction. It has been used widely in many applications involving high-dimensional data, such as face recognition and image retrieval. An intrinsic limitation of classical LDA is the so-called singularity problem, that is, it fails when all scatter matrices are singular. A well-known approach to deal with the singularity problem is to apply an intermediate dimension reduction stage using Principal Component Analysis (PCA) before LDA. The algorithm, called PCA LDA, is used widely in face recognition. However, PCA LDA has high costs in time and space, due to the need for an eigen-decomposition involving the scatter matrices. In this paper, we propose a novel LDA algorithm, namely 2DLDA, which stands for 2-Dimensional Linear Discriminant Analysis.

This paper analyzes generalization of the classic Rescorla-Wagner (R-W) learning algorithm and studies their relationship to Maximum Likelihood estimation of causal parameters. We prove that the parameters of two popular causal models, P and P C, can be learnt by the same generalized linear Rescorla-Wagner (GLRW) algorithm provided genericity conditions apply. We characterize the fixed points of these GLRW algorithms and calculate the fluctuations about them, assuming that the input is a set of i.i.d.

We relate the algorithm to the stochastic approximation literature. This enables us to specify conditions under which the algorithm is guaranteed to converge to the optimal solution (with probability 1). This includes necessary and sufficient conditions for the solution to be unbiased.

We study a number of open issues in spectral clustering: (i) Selecting the appropriate scale of analysis, (ii) Handling multi-scale data, (iii) Clustering with irregular background clutter, and, (iv) Finding automatically the number of groups. We first propose that a'local' scale should be used to compute the affinity between each pair of points. This local scaling leads to better clustering especially when the data includes multiple scales and when the clusters are placed within a cluttered background. We further suggest exploiting the structure of the eigenvectors to infer automatically the number of groups. This leads to a new algorithm in which the final randomly initialized k-means stage is eliminated.

Such a complexity is significant even for moderate size problems and is prohibitive for large datasets. We present an approximation technique based on the improved fast Gauss transform to reduce the computation to O(N). We also give an error bound for the approximation, and provide experimental results on the UCI datasets.

In this paper, we use the rollout method for policy improvement to analyze a version of Klondike solitaire. This version, sometimes called thoughtful solitaire, has all cards revealed to the player, but then follows the usual Klondike rules. A strategy that we establish, using iterated rollouts, wins about twice as many games on average as an expert human player does.

In this paper, we explore the use of Random Forests (RFs) in the structured language model (SLM), which uses rich syntactic information in predicting the next word based on words already seen. The goal in this work is to construct RFs by randomly growing Decision Trees (DTs) using syntactic information and investigate the performance of the SLM modeled by the RFs in automatic speech recognition. RFs, which were originally developed as classifiers, are a combination of decision tree classifiers. Each tree is grown based on random training data sampled independently and with the same distribution for all trees in the forest, and a random selection of possible questions at each node of the decision tree. Our approach extends the original idea of RFs to deal with the data sparseness problem encountered in language modeling. RFs have been studied in the context of n-gram language modeling and have been shown to generalize well to unseen data. We show in this paper that RFs using syntactic information can also achieve better performance in both perplexity (PPL) and word error rate (WER) in a large vocabulary speech recognition system, compared to a baseline that uses Kneser-Ney smoothing.

We propose a new method for clustering based on finding maximum margin hyperplanes through data. By reformulating the problem in terms of the implied equivalence relation matrix, we can pose the problem as a convex integer program. Although this still yields a difficult computational problem, the hard-clustering constraints can be relaxed to a soft-clustering formulation which can be feasibly solved with a semidefinite program. Since our clustering technique only depends on the data through the kernel matrix, we can easily achieve nonlinear clusterings in the same manner as spectral clustering. Experimental results show that our maximum margin clustering technique often obtains more accurate results than conventional clustering methods. The real benefit of our approach, however, is that it leads naturally to a semi-supervised training method for support vector machines. By maximizing the margin simultaneously on labeled and unlabeled training data, we achieve state of the art performance by using a single, integrated learning principle.

Linear Discriminant Analysis (LDA) is a well-known method for feature extraction and dimension reduction. It has been used widely in many applications such as face recognition. Recently, a novel LDA algorithm based on QR Decomposition, namely LDA/QR, has been proposed, which is competitive in terms of classification accuracy with other LDA algorithms, but it has much lower costs in time and space. However, LDA/QR is based on linear projection, which may not be suitable for data with nonlinear structure. This paper first proposes an algorithm called KDA/QR, which extends the LDA/QR algorithm to deal with nonlinear data by using the kernel operator. Then an efficient approximation of KDA/QR called AKDA/QR is proposed. Experiments on face image data show that the classification accuracy of both KDA/QR and AKDA/QR are competitive with Generalized Discriminant Analysis (GDA), a general kernel discriminant analysis algorithm, while AKDA/QR has much lower time and space costs.