Managing risk in dynamic decision problems is of cardinal importance in many fields such as finance and process control. The most common approach to defining risk is through various variance related criteria such as the Sharpe Ratio or the standard deviation adjusted reward. It is known that optimizing many of the variance related risk criteria is NP-hard. In this paper we devise a framework for local policy gradient style algorithms for reinforcement learning for variance related criteria. Our starting point is a new formula for the variance of the cost-to-go in episodic tasks. Using this formula we develop policy gradient algorithms for criteria that involve both the expected cost and the variance of the cost. We prove the convergence of these algorithms to local minima and demonstrate their applicability in a portfolio planning problem.

We study the problem of supervised linear dimensionality reduction, taking an information-theoretic viewpoint. The linear projection matrix is designed by maximizing the mutual information between the projected signal and the class label (based on a Shannon entropy measure). By harnessing a recent theoretical result on the gradient of mutual information, the above optimization problem can be solved directly using gradient descent, without requiring simplification of the objective function. Theoretical analysis and empirical comparison are made between the proposed method and two closely related methods (Linear Discriminant Analysis and Information Discriminant Analysis), and comparisons are also made with a method in which Renyi entropy is used to define the mutual information (in this case the gradient may be computed simply, under a special parameter setting). Relative to these alternative approaches, the proposed method achieves promising results on real datasets.

Differential privacy is a cryptographically-motivated definition of privacy which has gained significant attention over the past few years. Differentially private solutions enforce privacy by adding random noise to a function computed over the data, and the challenge in designing such algorithms is to control the added noise in order to optimize the privacy-accuracy-sample size tradeoff. This work studies differentially-private statistical estimation, and shows upper and lower bounds on the convergence rates of differentially private approximations to statistical estimators. Our results reveal a formal connection between differential privacy and the notion of Gross Error Sensitivity (GES) in robust statistics, by showing that the convergence rate of any differentially private approximation to an estimator that is accurate over a large class of distributions has to grow with the GES of the estimator. We then provide an upper bound on the convergence rate of a differentially private approximation to an estimator with bounded range and bounded GES. We show that the bounded range condition is necessary if we wish to ensure a strict form of differential privacy.

We investigate the problem of modeling symbolic sequences of polyphonic music in a completely general piano-roll representation. We introduce a probabilistic model based on distribution estimators conditioned on a recurrent neural network that is able to discover temporal dependencies in high-dimensional sequences. Our approach outperforms many traditional models of polyphonic music on a variety of realistic datasets. We show how our musical language model can serve as a symbolic prior to improve the accuracy of polyphonic transcription.

Much information available on the web is copied, reused or rephrased. The phenomenon that multiple web sources pick up certain information is often called trend. A central problem in the context of web data mining is to detect those web sources that are first to publish information which will give rise to a trend. We present a simple and efficient method for finding trends dominating a pool of web sources and identifying those web sources that publish the information relevant to a trend before others. We validate our approach on real data collected from influential technology news feeds.

We present a non-parametric Bayesian approach to structure learning with hidden causes. Previous Bayesian treatments of this problem define a prior over the number of hidden causes and use algorithms such as reversible jump Markov chain Monte Carlo to move between solutions. In contrast, we assume that the number of hidden causes is unbounded, but only a finite number influence observable variables. This makes it possible to use a Gibbs sampler to approximate the distribution over causal structures. We evaluate the performance of both approaches in discovering hidden causes in simulated data, and use our non-parametric approach to discover hidden causes in a real medical dataset.

This paper derives new bounds for the probabilities of causation defined by Pearl (2000), namely, the probability that one observed event was a necessary (or sufficient, or both) cause of another. Tian and Pearl (2000a, 2000b) showed how to bound these probabilities using information from experimental and observational studies,with minimal assumptions about the data-generating process. We derive narrower bounds using covariates measurements that might be available in the studies. In addition, we provide identifiable case under no-prevention assumption and discuss the covariate selection problem from the viewpoint of estimation accuracy. These results provides more accurate information for public policy, legal determination of responsibility and personal decision making.

There are several existing algorithms that under appropriate assumptions can reliably identify a subset of the underlying causal relationships from observational data. This paper introduces the first computationally feasible score-based algorithm that can reliably identify causal relationships in the large sample limit for discrete models, while allowing for the possibility that there are unobserved common causes. In doing so, the algorithm does not ever need to assign scores to causal structures with unobserved common causes. The algorithm is based on the identification of so called Y substructures within Bayesian network structures that can be learned from observational data. An example of a Y substructure is A -> C, B -> C, C -> D. After providing background on causal discovery, the paper proves the conditions under which the algorithm is reliable in the large sample limit.

Previous work in hierarchical reinforcement learning has faced a dilemma: either ignore the values of different possible exit states from a subroutine, thereby risking suboptimal behavior, or represent those values explicitly thereby incurring a possibly large representation cost because exit values refer to nonlocal aspects of the world (i.e., all subsequent rewards). This paper shows that, in many cases, one can avoid both of these problems. The solution is based on recursively decomposing the exit value function in terms of Q-functions at higher levels of the hierarchy. This leads to an intuitively appealing runtime architecture in which a parent subroutine passes to its child a value function on the exit states and the child reasons about how its choices affect the exit value. We also identify structural conditions on the value function and transition distributions that allow much more concise representations of exit state distributions, leading to further state abstraction. In essence, the only variables whose exit values need be considered are those that the parent cares about and the child affects. We demonstrate the utility of our algorithms on a series of increasingly complex environments.

Collaborative data consist of ratings relating two distinct sets of objects: users and items. Much of the work with such data focuses on filtering: predicting unknown ratings for pairs of users and items. In this paper we focus on the problem of visualizing the information. Given all of the ratings, our task is to embed all of the users and items as points in the same Euclidean space. We would like to place users near items that they have rated (or would rate) high, and far away from those they would give low ratings. We pose this problem as a real-valued nonlinear Bayesian network and employ Markov chain Monte Carlo and expectation maximization to find an embedding. We present a metric by which to judge the quality of a visualization and compare our results to Eigentaste, locally linear embedding and cooccurrence data embedding on three real-world datasets.