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High-Dimensional Statistics
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These lecture notes were written for the course 18.657, High Dimensional Statistics at MIT. They build on a set of notes that was prepared at Princeton University in 2013-14 that was modified (and hopefully improved) over the years.
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Cited by 11 Pith papers
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Variance-Reduced Q-Learning over Static and Time-Varying Networks
VRDQ achieves the optimal collaborative error rate 1/√(NT) for decentralized tabular Q-learning while requiring only O(log²(NT)) communication per agent, on both static and time-varying networks.
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Random measurements are almost maximally incompatible
Random two-outcome and basis measurements in high dimension are, with high probability, within a constant or logarithmic factor of the maximum possible measurement incompatibility, and the known scaling regimes for th...
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Sample complexity of Schr\"odinger potential estimation
An empirical KL minimizer over log-potentials estimates Schrödinger bridge potentials with terminal excess KL risk O(log^2 n / n) in the realizable case, even when the target distribution has unbounded support.
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Optimal community detection in dense bipartite graphs
The minimax separation rate for detecting a planted dense k1 by k2 subgraph in an n1 by n2 bipartite Erdős-Renyi graph is established up to constants under a dense-graph assumption.
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Convergence of Stochastic Gradient Methods for Wide Two-Layer Physics-Informed Neural Networks for the Poisson Equation
SGD and stochastic gradient flow are proven to drive the empirical PINN loss for the Poisson equation to zero exponentially in expectation, for sufficiently wide two-layer networks.
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Joint Planning and Operations of Wind Power under Decision-dependent Uncertainty
A two-stage distributionally robust wind farm planning model with a decision-dependent Wasserstein ambiguity set, reformulated as a mixed-integer second-order cone program with an accelerated constraint generation solver.
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Optimal Transport with Heterogeneously Missing Data
A debiased Bures-Wasserstein estimator and a matrix-completion based estimator for entropic optimal transport are consistent under heterogeneous MCAR missingness.
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Thompson Sampling-like Algorithms for Stochastic Rising Bandits
Thompson sampling with Beta or Gaussian priors and forced exploration achieves sublinear regret in stochastic rising rested bandits, with a new instance-complexity index sigma controlling the cost.
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How Private is Your Attention? Bridging Privacy with In-Context Learning
Differentially private pretraining of linear attention heads for in-context linear regression has excess risk that decays like 1/(N L^3) in low dimensions and D^2/(N^2 L^2) in high dimensions, up to log factors and pr...
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In-context denoising with one-layer transformers: connections between attention and associative memory retrieval
Softmax attention with identity weights is the Bayes optimal denoiser for spherical data, and trained one-layer transformers learn such weights.
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Leveraging Sparsity for Sample-Efficient Preference Learning: A Theoretical Perspective
For the sparse random utility model, the paper claims the minimax estimation rate is Θ((k/n) log(d/k)) and analyzes ℓ1-regularized estimators that come close to it.
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