Yuille's algorithm is based on a certain decomposition of the Bethe

Motivated by our recent work on rooted tree matching, in this paper we provide a solution to the problem of matching two free (i.e., unrooted) trees by constructing an association graph whose maximal cliques are in one-to-one correspondence with maximal common subtrees. We then solve the problem using simple replicator dynamics from evolutionary game theory. Experiments on hundreds of uniformly random trees are presented. The results are impressive: despite the inherent inability of these simple dynamics to escape from local optima, they always returned a globally optimal solution.

We present Linear Relational Embedding (LRE), a new method of learning adistributed representation of concepts from data consisting of instances ofrelations between given concepts. Its final goal is to be able to generalize, i.e. infer new instances of these relations among the concepts. Ona task involving family relationships we show that LRE can generalize better than any previously published method. We then show how LRE can be used effectively to find compact distributed representations forvariable-sized recursive data structures, such as trees and lists.

First, there are a wide variety of algorithms that use the eigenvectors in slightly different ways. Second, many of these algorithms have no proof that they will actually compute a reasonable clustering. In this paper, we present a simple spectral clustering algorithm that can be implemented using a few lines of Matlab. Using tools from matrix perturbation theory, we analyze the algorithm, and give conditions under which it can be expected to do well. We also show surprisingly good experimental results on a number of challenging clustering problems.

Discriminative classifiers model the posterior p(ylx)directly, or learn a direct map from inputs x to the class labels. There are several compelling reasons for using discriminative rather than generative classifiers, oneof which, succinctly articulated by Vapnik [6], is that "one should solve the [classification] problem directly and never solve a more general problem as an intermediate step [such as modeling p(xly)]." Indeed, leaving aside computational issues and matters such as handling missing data, the prevailing consensus seems to be that discriminative classifiers are almost always to be preferred to generative ones. Anotherpiece of prevailing folk wisdom is that the number of examples needed to fit a model is often roughly linear in the number of free parameters of a model. This has its theoretical basis in the observation that for "many" models, the VC dimension is roughly linear or at most some low-order polynomial in the number of parameters (see, e.g., [1, 3]), and it is known that sample complexity in the discriminative setting is linear in the VC dimension [6]. In this paper, we study empirically and theoretically the extent to which these beliefs are true. A parametric family of probabilistic models p(x, y) can be fit either to optimize the joint likelihood of the inputs and the labels, or fit to optimize the conditional likelihood p(ylx), or even fit to minimize the 0-1 training error obtained by thresholding p(ylx) to make predictions.

The hierarchical hidden Markov model (HHMM) is a generalization of the hidden Markov model (HMM) that models sequences with structure at many length/time scales [FST98].

We suggest a nonparametric framework for unsupervised learning of projection models in terms of density estimation on quantized sample spaces. The objective is not to optimally reconstruct the data but instead thequantizer is chosen to optimally reconstruct the density of the data. For the resulting quantizing density estimator (QDE) we present a general method for parameter estimation and model selection. We show how projection sets which correspond to traditional unsupervised methods likevector quantization or PCA appear in the new framework. For a principal component quantizer we present results on synthetic and realworld data,which show that the QDE can improve the generalization of the kernel density estimator although its estimate is based on significantly lower-dimensional projection indices of the data.

The algorithm is the first to compute equilibria both efficiently and exactly for a nontrivial class of graphical games. 1 Introduction Seeking to replicate the representational and computational benefits that graphical modelshave provided to probabilistic inference, several recent works have introduced graph-theoretic frameworks for the study of multi-agent systems (LaMura 2000; Koller and Milch 2001; Kearns et al. 2001). In the simplest of these formalisms, each vertex represents a single agent, and the edges represent pairwise interaction between agents. As with many familiar network models, the macroscopic behavior of a large system is thus implicitly described by its local interactions, andthe computational challenge is to extract the global states of interest. Classical game theory is typically used to model multi-agent interactions, and the global states of interest are thus the so-called Nash equilibria, in which no agent has a unilateral incentive to deviate. In a recent paper (Kearns et al. 2001), we introduced such a graphical formalism for multi-agent game theory, and provided two algorithms for computing Nash equilibria whenthe underlying graph is a tree (or is sufficiently sparse).

We present a new approach to bounding the true error rate of a continuous valued classifier based upon PAC-Bayes bounds. The method first constructs adistribution over classifiers by determining how sensitive each parameter in the model is to noise. The true error rate of the stochastic classifier found with the sensitivity analysis can then be tightly bounded using a PAC-Bayes bound.

When constructing a classifier, the probability of correct classification offuture data points should be maximized. In the current paper this desideratum is translated in a very direct way into an optimization problem, which is solved using methods from convex optimization.We also show how to exploit Mercer kernels in this setting to obtain nonlinear decision boundaries. A worst-case bound on the probability of misclassification of future data is obtained explicitly. 1 Introduction Consider the problem of choosing a linear discriminant by minimizing the probabilities thatdata vectors fall on the wrong side of the boundary. One way to attempt to achieve this is via a generative approach in which one makes distributional assumptions aboutthe class-conditional densities and thereby estimates and controls the relevant probabilities. The need to make distributional assumptions, however, casts doubt on the generality and validity of such an approach, and in discriminative solutionsto classification problems it is common to attempt to dispense with class-conditional densities entirely.