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.

Choice-based conjoint analysis builds models of consumer preferences over products with answers gathered in questionnaires. Our main goal is to bring tools from the machine learning community to solve this problem more efficiently. Thus, we propose two algorithms to quickly and accurately estimate consumer preferences.

High retrieval precision in content-based image retrieval can be attained by adopting relevance feedback mechanisms. These mechanisms require that the user judges the quality of the results of the query by marking all the retrieved images as being either relevant or not. Then, the search engine exploits this information to adapt the search to better meet user's needs. At present, the vast majority of proposed relevance feedback mechanisms are formulated in terms of search model that has to be optimized. Such an optimization involves the modification of some search parameters so that the nearest neighbor of the query vector contains the largest number of relevant images.

We present a competitive analysis of Bayesian learning algorithms in the online learning setting and show that many simple Bayesian algorithms (such as Gaussian linear regression and Bayesian logistic regression) perform favorably when compared, in retrospect, to the single best model in the model class. The analysis does not assume that the Bayesian algorithms' modeling assumptions are "correct," and our bounds hold even if the data is adversarially chosen. For Gaussian linear regression (using logloss), our error bounds are comparable to the best bounds in the online learning literature, and we also provide a lower bound showing that Gaussian linear regression is optimal in a certain worst case sense. We also give bounds for some widely used maximum a posteriori (MAP) estimation algorithms, including regularized logistic regression.

A reactive environment is one that responds to the actions of an agent rather than evolving obliviously. In reactive environments, experts algorithms must balance exploration and exploitation of experts more carefully than in oblivious ones. In addition, a more subtle definition of a learnable value of an expert is required. A general exploration-exploitation experts method is presented along with a proper definition of value. The method is shown to asymptotically perform as well as the best available expert. Several variants are analyzed from the viewpoint of the exploration-exploitation tradeoff, including explore-then-exploit, polynomially vanishing exploration, constant-frequency exploration, and constant-size exploration phases. Complexity and performance bounds are proven.

This paper presents an application of Boosting for classifying labeled graphs, general structures for modeling a number of real-world data, such as chemical compounds, natural language texts, and bio sequences. The proposal consists of i) decision stumps that use subgraph as features, and ii) a Boosting algorithm in which subgraph-based decision stumps are used as weak learners. We also discuss the relation between our algorithm and SVMs with convolution kernels. Two experiments using natural language data and chemical compounds show that our method achieves comparable or even better performance than SVMs with convolution kernels as well as improves the testing efficiency.

Agents learning to act in a partially observable domain may need to overcome the problem of perceptual aliasing - i.e., different states that appear similar but require different responses. This problem is exacerbated when the agent's sensors are noisy, i.e., sensors may produce different observations in the same state. We show that many well-known reinforcement learning methods designed to deal with perceptual aliasing, such as Utile Suffix Memory, finite size history windows, eligibility traces, and memory bits, do not handle noisy sensors well. We suggest a new algorithm, Noisy Utile Suffix Memory (NUSM), based on USM, that uses a weighted classification of observed trajectories. We compare NUSM to the above methods and show it to be more robust to noise.

We propose the hierarchical Dirichlet process (HDP), a nonparametric Bayesian model for clustering problems involving multiple groups of data. Each group of data is modeled with a mixture, with the number of components being open-ended and inferred automatically by the model. Further, components can be shared across groups, allowing dependencies across groups to be modeled effectively as well as conferring generalization to new groups. Such grouped clustering problems occur often in practice, e.g. in the problem of topic discovery in document corpora. We report experimental results on three text corpora showing the effective and superior performance of the HDP over previous models.

In this paper we argue that the choice of the SVM cost parameter can be critical. We then derive an algorithm that can fit the entire path of SVM solutions for every value of the cost parameter, with essentially the same computational cost as fitting one SVM model.

We present a discriminative part-based approach for the recognition of object classes from unsegmented cluttered scenes. Objects are modeled as flexible constellations of parts conditioned on local observations found by an interest operator. For each object class the probability of a given assignment of parts to local features is modeled by a Conditional Random Field (CRF). We propose an extension of the CRF framework that incorporates hidden variables and combines class conditional CRFs into a unified framework for part-based object recognition. The parameters of the CRF are estimated in a maximum likelihood framework and recognition proceeds by finding the most likely class under our model. The main advantage of the proposed CRF framework is that it allows us to relax the assumption of conditional independence of the observed data (i.e.