In this work, we consider the problem of learning a positive semidefinite matrix. The critical issue is how to preserve positive semidefiniteness during the course of learning. Our algorithm is mainly inspired by LPBoost [1] and the general greedy convex optimization framework of Zhang [2]. We demonstrate the essence of the algorithm, termed PSDBoost (positive semidefinite Boosting), by focusing on a few different applications in machine learning. The proposed PSDBoost algorithm extends traditional Boosting algorithms in that its parameter is a positive semidefinite matrix with trace being one instead of a classifier. PSDBoost is based on the observation that any trace-one positive semidefinitematrix can be decomposed into linear convex combinations of trace-one rank-one matrices, which serve as base learners of PSDBoost. Numerical experiments are presented.

We present a new reinforcement-learning model for the role of the hippocampus in classical conditioning, focusing on the differences between trace and delay conditioning. In the model, all stimuli are represented both as unindividuated wholes and as a series of temporal elements with varying delays. These two stimulus representations interact, producing different patterns of learning in trace and delay conditioning. The model proposes that hippocampal lesions eliminate long-latency temporal elements, but preserve short-latency temporal elements. For trace conditioning, with no contiguity between stimulus and reward, these long-latency temporal elements are vital to learning adaptively timed responses. For delay conditioning, in contrast, the continued presence of the stimulus supports conditioned responding, and the short-latency elements suppress responding early in the stimulus. In accord with the empirical data, simulated hippocampal damage impairs trace conditioning, but not delay conditioning, at medium-length intervals. With longer intervals, learning is impaired in both procedures, and, with shorter intervals, in neither. In addition, the model makes novel predictions about the response topography with extended stimuli or post-training lesions. These results demonstrate how temporal contiguity, as in delay conditioning, changes the timing problem faced by animals, rendering it both easier and less susceptible to disruption by hippocampal lesions.

In this paper we introduce a new algorithm for updating the parameters of a heuristic evaluation function, by updating the heuristic towards the values computed by an alpha-beta search. Our algorithm differs from previous approaches to learning from search, such as Samuels checkers player and the TD-Leaf algorithm, in two key ways. First, we update all nodes in the search tree, rather than a single node. Second, we use the outcome of a deep search, instead of the outcome of a subsequent search, as the training signal for the evaluation function. We implemented our algorithm in a chess program Meep, using a linear heuristic function. After initialising its weight vector to small random values, Meep was able to learn high quality weights from self-play alone. When tested online against human opponents, Meep played at a master level, the best performance of any chess program with a heuristic learned entirely from self-play.

The learning of appropriate distance metrics is a critical problem in classification. In this work, we propose a boosting-based technique, termed BoostMetric, for learning a Mahalanobis distance metric. One of the primary difficulties in learning such a metric is to ensure that the Mahalanobis matrix remains positive semidefinite. Semidefinite programming is sometimes used to enforce this constraint, but does not scale well. BoostMetric is instead based on a key observation that any positive semidefinite matrix can be decomposed into a linear positive combination of trace-one rank-one matrices. BoostMetric thus uses rank-one positive semidefinite matrices as weak learners within an efficient and scalable boosting-based learning process. The resulting method is easy to implement, does not require tuning, and can accommodate various types of constraints. Experiments on various datasets show that the proposed algorithm compares favorably to those state-of-the-art methods in terms of classification accuracy and running time.

We present polynomial-time algorithms for the exact computation of lowest- energy states, worst margin violators, partition functions, and marginals in binary undirected graphical models. Our approach provides an interesting alternative to the well-known graph cut paradigm in that it does not impose any submodularity constraints; instead we require planarity to establish a correspondence with perfect matchings in an expanded dual graph. Maximum-margin parameter estimation for a boundary detection task shows our approach to be efficient and effective.

Many machine learning algorithms can be formulated in the framework of statistical independence such as the Hilbert Schmidt Independence Criterion. In this paper, we extend this criterion to deal with with structured and interdependent observations. This is achieved by modeling the structures using undirected graphical models and comparing the Hilbert space embeddings of distributions. We apply this new criterion to independent component analysis and sequence clustering.

Object matching is a fundamental operation in data analysis. It typically requires the definition of a similarity measure between the classes of objects to be matched. Instead, we develop an approach which is able to perform matching by requiring a similarity measure only within each of the classes. This is achieved by maximizing the dependency between matched pairs of observations by means of the Hilbert Schmidt Independence Criterion. This problem can be cast as one of maximizing a quadratic assignment problem with special structure and we present a simple algorithm for finding a locally optimal solution.

We present a novel and highly effective approach for multi-body motion segmentation. Drawing inspiration from robust statistical model fitting, we estimate putative subspace hypotheses from the data. However, instead of ranking them we encapsulate the hypotheses in a novel Mercer kernel which elicits the potential of two point trajectories to have emerged from the same subspace. The kernel permits the application of well-established statistical learning methods for effective outlier rejection, automatic recovery of the number of motions and accurate segmentation of the point trajectories. The method operates well under severe outliers arising from spurious trajectories or mistracks. Detailed experiments on a recent benchmark dataset (Hopkins 155) show that our method is superior to other state-of-the-art approaches in terms of recovering the number of motions, segmentation accuracy, robustness against gross outliers and computational efficiency.

Secure networks rely upon players to maintain security and reliability. However not every player can be assumed to have total loyalty and one must use methods to uncover traitors in such networks. We use the original concept of the Byzantine Generals Problem by Lamport, and the more formal Byzantine Agreement describe by Linial, to nd traitors in secure networks. By applying general fault-tolerance methods to develop a more formal design of secure networks we are able to uncover traitors amongst a group of players. We also propose methods to integrate this system with insecure channels. This new resiliency can be applied to broadcast and peer-to-peer secure communication systems where agents may be traitors or become unreliable due to faults.

In Dempster-Shafer belief theory, general beliefs are expressed as belief mass distribution functions over frames of discernment. In Subjective Logic beliefs are expressed as belief mass distribution functions over binary frames of discernment. Belief representations in Subjective Logic, which are called opinions, also contain a base rate parameter which express the a priori belief in the absence of evidence. Philosophically, beliefs are quantitative representations of evidence as perceived by humans or by other intelligent agents. The basic operators of classical probability calculus, such as addition and multiplication, can be applied to opinions, thereby making belief calculus practical. Through the equivalence between opinions and Beta probability density functions, this also provides a calculus for Beta probability density functions. This article explains the basic elements of belief calculus.