A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
We consider the fundamental learning problem of estimating properties of distributions over large domains. Using a novel piecewise-polynomial approximation technique, we derive the first unified methodology for constructing sample- and time-efficient estimators for all sufficiently smooth, symmetric and non-symmetric, …
In this paper, we consider the problem of learning an unknown graph via queries on groups of nodes, with the result indicating whether or not at least one edge is present among those nodes. While learning arbitrary graphs with n nodes and k edges is known to be hard in the sense of requiring $Ω( \min\{ k^2 \log n, …
In the context of clustering, we consider a generative model in a Euclidean ambient space with clusters of different shapes, dimensions, sizes and densities. In an asymptotic setting where the number of points becomes large, we obtain theoretical guaranties for a few emblematic methods based on pairwise distances: a si…
In this paper, we study the trace regression when a matrix of parameters B* is estimated via the convex relaxation of a rank-regularized regression or via regularized non-convex optimization. It is known that these estimators satisfy near-optimal error bounds under assumptions on the rank, coherence, and spikiness of B…
We provide a general theory of the expectation-maximization (EM) algorithm for inferring high dimensional latent variable models. In particular, we make two contributions: (i) For parameter estimation, we propose a novel high dimensional EM algorithm which naturally incorporates sparsity structure into parameter estima…
Stochastic optimization naturally arises in machine learning. Efficient algorithms with provable guarantees, however, are still largely missing, when the objective function is nonconvex and the data points are dependent. This paper studies this fundamental challenge through a streaming PCA problem for stationary time s…
We study the worst-case adaptive optimization problem with budget constraint that is useful for modeling various practical applications in artificial intelligence and machine learning. We investigate the near-optimality of greedy algorithms for this problem with both modular and non-modular cost functions. In both case…
We study the problem of detecting a change in the mean of one-dimensional Gaussian process data. This problem is investigated in the setting of increasing domain (customarily employed in time series analysis) and in the setting of fixed domain (typically arising in spatial data analysis). We propose a detection method …
Active Reinforcement Learning (ARL) is a twist on RL where the agent observes reward information only if it pays a cost. This subtle change makes exploration substantially more challenging. Powerful principles in RL like optimism, Thompson sampling, and random exploration do not help with ARL. We relate ARL in tabular …
We study the problem of regret minimization for distributed bandits learning, in which M agents work collaboratively to minimize their total regret under the coordination of a central server. Our goal is to design communication protocols with near-optimal regret and little communication cost, which is measured by the…
Efficiently find near-optimal medical treatments with less trial and error.
problem Finding effective medical treatments through trial and error.
method Formalizes the problem, uses a causal inference framework, and proposes model-based dynamic programming and greedy algorithms.
result Our methods compare favorably to model-free reinforcement learning, offering a more transparent trade-off between search time and treatment efficacy.
Estimates and infers multi-stage stationary treatment policies with variable selection.
problem Valid inference for multi-stage stationary treatment policies with high-dimensional feature variables.
method Estimate the value function using augmented inverse probability weighted estimator, apply penalty for variable selection, construct one-step improvements for valid inference.
result Improved estimators are asymptotically normal, valid inference for policy parameters demonstrated.