Sham M. Kakade

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This work considers a computationally and statistically efficient parameter estimation method for a wide class of latent variable models—including Gaussian mixture models, hidden Markov models, and latent Dirichlet allocation—which exploits a certain tensor structure in their low-order observable moments (typically, of secondand third-order). Specifically,(More)
Many applications require optimizing an unknown, noisy function that is expensive to evaluate. We formalize this task as a multiarmed bandit problem, where the payoff function is either sampled from a Gaussian process (GP) or has low RKHS norm. We resolve the important open problem of deriving regret bounds for this setting, which imply novel convergence(More)
This thesis is a detailed investigation into the following question: how much data must an agent collect in order to perform “reinforcement learning” successfully? This question is analogous to the classical issue of the sample complexity in supervised learning, but is harder because of the increased realism of the reinforcement learning setting. This(More)
We provide a natural gradient method that represents the steepest descent direction based on the underlying structure of the parameter space. Although gradient methods cannot make large changes in the values of the parameters, we show that the natural gradient is moving toward choosing a greedy optimal action rather than just a better action. These greedy(More)
We consider multi-label prediction problems with large output spaces under the assumption of output sparsity – that the target (label) vectors have small support. We develop a general theory for a variant of the popular error correcting output code scheme, using ideas from compressed sensing for exploiting this sparsity. The method can be regarded as a(More)
Mixture models are a fundamental tool in applied statistics and machine learning for treating data taken from multiple subpopulations. The current practice for estimating the parameters of such models relies on local search heuristics (e.g., the EM algorithm) which are prone to failure, and existing consistent methods are unfavorable due to their high(More)
In the classical stochastic k-armed bandit problem, in each of a sequence of rounds, a decision maker chooses one of k arms and incurs a cost chosen from an unknown distribution associated with that arm. In the linear optimization analog of this problem, rather than finitely many arms, the decision set is a compact subset of R and the cost of each decision(More)
Clustering data in high dimensions is believed to be a hard problem in general. A number of efficient clustering algorithms developed in recent years address this problem by projecting the data into a lower-dimensional subspace, e.g. via Principal Components Analysis (PCA) or random projections, before clustering. Here, we consider constructing such(More)