Psychophysical experiments show that humans are better at perceiving rotation and expansion than translation. These findings are inconsistent with standard models of motion integration which predict best performance for translation [6]. To explain this discrepancy, our theory formulates motion perception at two levels of inference: we first perform model selection between the competing models (e.g. We define novel prior models for smooth rotation and expansion using techniques similar to those in the slow-and-smooth model [17] (e.g. Green functions of differential operators). The theory gives good agreement with the trends observed in human experiments.

In solving complex visual learning tasks, adopting multiple descriptors to more precisely characterize the data has been a feasible way for improving performance. These representations are typically high dimensional and assume diverse forms. Thus finding a way to transform them into a unified space of lower dimension generally facilitates the underlying tasks, such as object recognition or clustering. We describe an approach that incorporates multiple kernel learning with dimensionality reduction (MKL-DR). While the proposed framework is flexible in simultaneously tackling data in various feature representations, the formulation itself is general in that it is established upon graph embedding.

In this paper we consider approximate policy-iteration-based reinforcement learning algorithms. In order to implement a flexible function approximation scheme we propose the use of non-parametric methods with regularization, providing a convenient way to control the complexity of the function approximator. We propose two novel regularized policy iteration algorithms by adding L2-regularization to two widely-used policy evaluation methods: Bellman residual minimization (BRM) and least-squares temporal difference learning (LSTD). We derive efficient implementation for our algorithms when the approximate value-functions belong to a reproducing kernel Hilbert space. We also provide finite-sample performance bounds for our algorithms and show that they are able to achieve optimal rates of convergence under the studied conditions.

Language comprehension in humans is significantly constrained by memory, yet rapid, highly incremental, and capable of utilizing a wide range of contextual information to resolve ambiguity and form expectations about future input. In contrast, most of the leading psycholinguistic models and fielded algorithms for natural language parsing are non-incremental, have run time superlinear in input length, and/or enforce structural locality constraints on probabilistic dependencies between events. We present a new limited-memory model of sentence comprehension which involves an adaptation of the particle filter, a sequential Monte Carlo method, to the problem of incremental parsing. We show that this model can reproduce classic results in online sentence comprehension, and that it naturally provides the first rational account of an outstanding problem in psycholinguistics, in which the preferred alternative in a syntactic ambiguity seems to grow more attractive over time even in the absence of strong disambiguating information.

In kernel-based regression learning, optimizing each kernel individually is useful when the data density, curvature of regression surfaces (or decision boundaries) or magnitude of output noise (i.e., heteroscedasticity) varies spatially. Unfortunately, it presents a complex computational problem as the danger of overfitting is high and the individual optimization of every kernel in a learning system may be overly expensive due to the introduction of too many open learning parameters. Previous work has suggested gradient descent techniques or complex statistical hypothesis methods for local kernel shaping, typically requiring some amount of manual tuning of meta parameters. In this paper, we focus on nonparametric regression and introduce a Bayesian formulation that, with the help of variational approximations, results in an EM-like algorithm for simultaneous estimation of regression and kernel parameters. The algorithm is computationally efficient (suitable for large data sets), requires no sampling, automatically rejects outliers and has only one prior to be specified.

In classification problems, Support Vector Machines maximize the margin of separation between two classes. While the paradigm has been successful, the solution obtained by SVMs is dominated by the directions with large data spread and biased to separate the classes by cutting along large spread directions. This article proposes a novel formulation to overcome such sensitivity and maximizes the margin relative to the spread of the data. The proposed formulation can be efficiently solved and experiments on digit datasets show drastic performance improvements over SVMs.

Kernel Principal Component Analysis (KPCA) is a popular generalization of linear PCA that allows non-linear feature extraction. In KPCA, data in the input space is mapped to higher (usually) dimensional feature space where the data can be linearly modeled. The feature space is typically induced implicitly by a kernel function, and linear PCA in the feature space is performed via the kernel trick. However, due to the implicitness of the feature space, some extensions of PCA such as robust PCA cannot be directly generalized to KPCA. This paper presents a technique to overcome this problem, and extends it to a unified framework for treating noise, missing data, and outliers in KPCA.

This paper addresses the important tradeoff between privacy and learnability, when designing algorithms for learning from private databases. First we apply an idea of Dwork et al. to design a specific privacy-preserving machine learning algorithm, logistic regression. This involves bounding the sensitivity of logistic regression, and perturbing the learned classifier with noise proportional to the sensitivity. Noting that the approach of Dwork et al. has limitations when applied to other machine learning algorithms, we then present another privacy-preserving logistic regression algorithm. The algorithm is based on solving a perturbed objective, and does not depend on the sensitivity.

Probabilistic topic models (and their extensions) have become popular as models of latent structures in collections of text documents or images. These models are usually treated as generative models and trained using maximum likelihood estimation, an approach which may be suboptimal in the context of an overall classification problem. In this paper, we describe DiscLDA, a discriminative learning framework for such models as Latent Dirichlet Allocation (LDA) in the setting of dimensionality reduction with supervised side information. In DiscLDA, a class-dependent linear transformation is introduced on the topic mixture proportions. This parameter is estimated by maximizing the conditional likelihood using Monte Carlo EM.

We analyse matching pursuit for kernel principal components analysis by proving that the sparse subspace it produces is a sample compression scheme. We show that this bound is tighter than the KPCA bound of Shawe-Taylor et al swck-05 and highly predictive of the size of the subspace needed to capture most of the variance in the data. We analyse a second matching pursuit algorithm called kernel matching pursuit (KMP) which does not correspond to a sample compression scheme. However, we give a novel bound that views the choice of subspace of the KMP algorithm as a compression scheme and hence provide a VC bound to upper bound its future loss. Finally we describe how the same bound can be applied to other matching pursuit related algorithms.