Computing Upper and Lower Bounds on Likelihoods in Intractable Networks

We present techniques for computing upper and lower bounds on the likelihoods of partial instantiations of variables in sigmoid and noisy-OR networks. The bounds determine confidence intervals for the desired likelihoods and become useful when the size of the network (or clique size) precludes exact computations. We illustrate the tightness of the obtained bounds by numerical experiments.

Risk Bounds for Mixture Density Estimation

In this paper we focus on the problem of estimating a bounded density using a finite combination of densities from a given class. We consider the Maximum Likelihood Procedure (MLE) and the greedy procedure described by Li and Barron. Approximation and estimation bounds are given for the above methods. We extend and improve upon the estimation results of Li and Barron, and in particular prove an $O(\\frac{1}{\\sqrt{n}})$ bound on the estimation error which does not depend on the number of densities in the estimated combination.

Lower Bounds for Achieving Synchronous Early Stopping Consensus with Orderly Crash Failures

In this paper, we discuss the consensus problem for synchronous distributed systems with orderly crash failures. For a synchronous distributed system of n processes with up to t crash failures and f failures actually occur, first, we present a bivalency argument proof to solve the open problem of proving the lower bound, min (t + 1, f + 2) rounds, for early-stopping synchronous consensus with orderly crash failures, where t < n - 1. Then, we extend the system model with orderly crash failures to a new model in which a process is allowed to send multiple messages to the same destination process in a round and the failing processes still respect the order specified by the protocol in sending messages. For this new model, we present a uniform consensus protocol, in which all non-faulty processes always decide and stop immediately by the end of f + 1 rounds. We prove that the lower bound of early stopping protocols for both consensus and uniform consensus are f + 1 rounds under the new model, and our proposed protocol is optimal.

Formalizing Triggers: A Learning Model for Finite Spaces

In a recent seminal paper, Gibson and Wexler (1993) take important steps to formalizing the notion of language learning in a (finite) space whose grammars are characterized by a finite number of parameters. They introduce the Triggering Learning Algorithm (TLA) and show that even in finite space convergence may be a problem due to local maxima. In this paper we explicitly formalize learning in finite parameter space as a Markov structure whose states are parameter settings. We show that this captures the dynamics of TLA completely and allows us to explicitly compute the rates of convergence for TLA and other variants of TLA e.g. random walk. Also included in the paper are a corrected version of GW's central convergence proof, a list of "problem states" in addition to local maxima, and batch and PAC-style learning bounds for the model.

The Essential Dynamics Algorithm: Essential Results

This paper presents a novel algorithm for learning in a class of stochastic Markov decision processes (MDPs) with continuous state and action spaces that trades speed for accuracy. A transform of the stochastic MDP into a deterministic one is presented which captures the essence of the original dynamics, in a sense made precise. In this transformed MDP, the calculation of values is greatly simplified. The online algorithm estimates the model of the transformed MDP and simultaneously does policy search against it. Bounds on the error of this approximation are proven, and experimental results in a bicycle riding domain are presented. The algorithm learns near optimal policies in orders of magnitude fewer interactions with the stochastic MDP, using less domain knowledge. All code used in the experiments is available on the project's web site.

Permutation Tests for Classification

We introduce and explore an approach to estimating statistical significance of classification accuracy, which is particularly useful in scientific applications of machine learning where high dimensionality of the data and the small number of training examples render most standard convergence bounds too loose to yield a meaningful guarantee of the generalization ability of the classifier. Instead, we estimate statistical significance of the observed classification accuracy, or the likelihood of observing such accuracy by chance due to spurious correlations of the high-dimensional data patterns with the class labels in the given training set. We adopt permutation testing, a non-parametric technique previously developed in classical statistics for hypothesis testing in the generative setting (i.e., comparing two probability distributions). We demonstrate the method on real examples from neuroimaging studies and DNA microarray analysis and suggest a theoretical analysis of the procedure that relates the asymptotic behavior of the test to the existing convergence bounds.

Mobilized ad-hoc networks: A reinforcement learning approach

Research in mobile ad-hoc networks has focused on situations in which nodes have no control over their movements. We investigate an important but overlooked domain in which nodes do have control over their movements. Reinforcement learning methods can be used to control both packet routing decisions and node mobility, dramatically improving the connectivity of the network. We first motivate the problem by presenting theoretical bounds for the connectivity improvement of partially mobile networks and then present superior empirical results under a variety of different scenarios in which the mobile nodes in our ad-hoc network are embedded with adaptive routing policies and learned movement policies.

Optimal Approximations of the Frequency Moments

We give a one-pass, O~(m^{1-2/k})-space algorithm for estimating the k-th frequency moment of a data stream for any real k>2. Together with known lower bounds, this resolves the main problem left open by Alon, Matias, Szegedy, STOC'96. Our algorithm enables deletions as well as insertions of stream elements.

Synthesizing Regularity Exposing Attributes in Large Protein Databases

This thesis describes a system that synthesizes regularity exposing attributes from large protein databases. After processing primary and secondary structure data, this system discovers an amino acid representation that captures what are thought to be the three most important amino acid characteristics (size, charge, and hydrophobicity) for tertiary structure prediction. A neural network trained using this 16 bit representation achieves a performance accuracy on the secondary structure prediction problem that is comparable to the one achieved by a neural network trained using the standard 24 bit amino acid representation. In addition, the thesis describes bounds on secondary structure prediction accuracy, derived using an optimal learning algorithm and the probably approximately correct (PAC) model.

Robust and Efficient 3D Recognition by Alignment

Alignment is a prevalent approach for recognizing 3D objects in 2D images. A major problem with current implementations is how to robustly handle errors that propagate from uncertainties in the locations of image features. This thesis gives a technique for bounding these errors. The technique makes use of a new solution to the problem of recovering 3D pose from three matching point pairs under weak-perspective projection. Furthermore, the error bounds are used to demonstrate that using line segments for features instead of points significantly reduces the false positive rate, to the extent that alignment can remain reliable even in cluttered scenes.

Robust 2-D Model-Based Object Recognition

Techniques, suitable for parallel implementation, for robust 2D model-based object recognition in the presence of sensor error are studied. Models and scene data are represented as local geometric features and robust hypothesis of feature matchings and transformations is considered. Bounds on the error in the image feature geometry are assumed constraining possible matchings and transformations. Transformation sampling is introduced as a simple, robust, polynomial-time, and highly parallel method of searching the space of transformations to hypothesize feature matchings. Key to the approach is that error in image feature measurement is explicitly accounted for. A Connection Machine implementation and experiments on real images are presented.