We consider a class of sparsity-inducing regularization terms based on submodular functions. While previous work has focused on non-decreasing functions, we explore symmetric submodular functions and their \lova extensions. We show that the Lovasz extension may be seen as the convex envelope of a function that depends on level sets (i.e., the set of indices whose corresponding components of the underlying predictor are greater than a given constant): this leads to a class of convex structured regularization terms that impose prior knowledge on the level sets, and not only on the supports of the underlying predictors. We provide a unified set of optimization algorithms, such as proximal operators, and theoretical guarantees (allowed level sets and recovery conditions). By selecting specific submodular functions, we give a new interpretation to known norms, such as the total variation; we also define new norms, in particular ones that are based on order statistics with application to clustering and outlier detection, and on noisy cuts in graphs with application to change point detection in the presence of outliers.

This study presents a method to discover an outbreak of an infectious disease in a region for which data are missing, but which is at work as a disease spreader. Node discovery for the spread of an infectious disease is defined as discriminating between the nodes which are neighboring to a missing disease spreader node, and the rest, given a dataset on the number of cases. The spread is described by stochastic differential equations. A perturbation theory quantifies the impact of the missing spreader on the moments of the number of cases. Statistical discriminators examine the mid-body or tail-ends of the probability density function, and search for the disturbance from the missing spreader. They are tested with computationally synthesized datasets, and applied to the SARS outbreak and flu pandemic.

We propose a logical/mathematical framework for statistical parameter learning of parameterized logic programs, i.e. definite clause programs containing probabilistic facts with a parameterized distribution. It extends the traditional least Herbrand model semantics in logic programming to distribution semantics, possible world semantics with a probability distribution which is unconditionally applicable to arbitrary logic programs including ones for HMMs, PCFGs and Bayesian networks. We also propose a new EM algorithm, the graphical EM algorithm, that runs for a class of parameterized logic programs representing sequential decision processes where each decision is exclusive and independent. It runs on a new data structure called support graphs describing the logical relationship between observations and their explanations, and learns parameters by computing inside and outside probability generalized for logic programs. The complexity analysis shows that when combined with OLDT search for all explanations for observations, the graphical EM algorithm, despite its generality, has the same time complexity as existing EM algorithms, i.e. the Baum-Welch algorithm for HMMs, the Inside-Outside algorithm for PCFGs, and the one for singly connected Bayesian networks that have been developed independently in each research field. Learning experiments with PCFGs using two corpora of moderate size indicate that the graphical EM algorithm can significantly outperform the Inside-Outside algorithm.

Common wisdom has it that small distinctions in the probabilities (parameters) quantifying a belief network do not matter much for the results of probabilistic queries. Yet, one can develop realistic scenarios under which small variations in network parameters can lead to significant changes in computed queries. A pending theoretical question is then to analytically characterize parameter changes that do or do not matter. In this paper, we study the sensitivity of probabilistic queries to changes in network parameters and prove some tight bounds on the impact that such parameters can have on queries. Our analytic results pinpoint some interesting situations under which parameter changes do or do not matter. These results are important for knowledge engineers as they help them identify influential network parameters. They also help explain some of the previous experimental results and observations with regards to network robustness against parameter changes.

Spoken dialogue systems promise efficient and natural access to a large variety of information sources and services from any phone. However, current spoken dialogue systems are deficient in their strategies for preventing, identifying and repairing problems that arise in the conversation. This paper reports results on automatically training a Problematic Dialogue Predictor to predict problematic human-computer dialogues using a corpus of 4692 dialogues collected with the 'How May I Help You' (SM) spoken dialogue system. The Problematic Dialogue Predictor can be immediately applied to the system's decision of whether to transfer the call to a human customer care agent, or be used as a cue to the system's dialogue manager to modify its behavior to repair problems, and even perhaps, to prevent them. We show that a Problematic Dialogue Predictor using automatically-obtainable features from the first two exchanges in the dialogue can predict problematic dialogues 13.2% more accurately than the baseline.

An approach to the construction of classifiers from imbalanced datasets is described. A dataset is imbalanced if the classification categories are not approximately equally represented. Often real-world data sets are predominately composed of "normal" examples with only a small percentage of "abnormal" or "interesting" examples. It is also the case that the cost of misclassifying an abnormal (interesting) example as a normal example is often much higher than the cost of the reverse error. Under-sampling of the majority (normal) class has been proposed as a good means of increasing the sensitivity of a classifier to the minority class. This paper shows that a combination of our method of over-sampling the minority (abnormal) class and under-sampling the majority (normal) class can achieve better classifier performance (in ROC space) than only under-sampling the majority class. This paper also shows that a combination of our method of over-sampling the minority class and under-sampling the majority class can achieve better classifier performance (in ROC space) than varying the loss ratios in Ripper or class priors in Naive Bayes. Our method of over-sampling the minority class involves creating synthetic minority class examples. Experiments are performed using C4.5, Ripper and a Naive Bayes classifier. The method is evaluated using the area under the Receiver Operating Characteristic curve (AUC) and the ROC convex hull strategy.

This paper discusses a system that accelerates reinforcement learning by using transfer from related tasks. Without such transfer, even if two tasks are very similar at some abstract level, an extensive re-learning effort is required. The system achieves much of its power by transferring parts of previously learned solutions rather than a single complete solution. The system exploits strong features in the multi-dimensional function produced by reinforcement learning in solving a particular task. These features are stable and easy to recognize early in the learning process. They generate a partitioning of the state space and thus the function. The partition is represented as a graph. This is used to index and compose functions stored in a case base to form a close approximation to the solution of the new task. Experiments demonstrate that function composition often produces more than an order of magnitude increase in learning rate compared to a basic reinforcement learning algorithm.

This paper addresses the problem of planning under uncertainty in large Markov Decision Processes (MDPs). Factored MDPs represent a complex state space using state variables and the transition model using a dynamic Bayesian network. This representation often allows an exponential reduction in the representation size of structured MDPs, but the complexity of exact solution algorithms for such MDPs can grow exponentially in the representation size. In this paper, we present two approximate solution algorithms that exploit structure in factored MDPs. Both use an approximate value function represented as a linear combination of basis functions, where each basis function involves only a small subset of the domain variables. A key contribution of this paper is that it shows how the basic operations of both algorithms can be performed efficiently in closed form, by exploiting both additive and context-specific structure in a factored MDP. A central element of our algorithms is a novel linear program decomposition technique, analogous to variable elimination in Bayesian networks, which reduces an exponentially large LP to a provably equivalent, polynomial-sized one. One algorithm uses approximate linear programming, and the second approximate dynamic programming. Our dynamic programming algorithm is novel in that it uses an approximation based on max-norm, a technique that more directly minimizes the terms that appear in error bounds for approximate MDP algorithms. We provide experimental results on problems with over 10^40 states, demonstrating a promising indication of the scalability of our approach, and compare our algorithm to an existing state-of-the-art approach, showing, in some problems, exponential gains in computation time.

We propose a perspective on knowledge compilation which calls for analyzing different compilation approaches according to two key dimensions: the succinctness of the target compilation language, and the class of queries and transformations that the language supports in polytime. We then provide a knowledge compilation map, which analyzes a large number of existing target compilation languages according to their succinctness and their polytime transformations and queries. We argue that such analysis is necessary for placing new compilation approaches within the context of existing ones. We also go beyond classical, flat target compilation languages based on CNF and DNF, and consider a richer, nested class based on directed acyclic graphs (such as OBDDs), which we show to include a relatively large number of target compilation languages.

Inductive logic programming, or relational learning, is a powerful paradigm for machine learning or data mining. However, in order for ILP to become practically useful, the efficiency of ILP systems must improve substantially. To this end, the notion of a query pack is introduced: it structures sets of similar queries. Furthermore, a mechanism is described for executing such query packs. A complexity analysis shows that considerable efficiency improvements can be achieved through the use of this query pack execution mechanism. This claim is supported by empirical results obtained by incorporating support for query pack execution in two existing learning systems.