Robust and High-Dimensional Statistics (Simons Institute workshop, 2018)
2018-10-29..2018-11-02
Berkeley, United States
[Information Theory, Learning and Big Data (Simons Institute, 2015), Optimization, Statistics and Uncertainty, Randomized Numerical Linear Algebra and Applications 2018, Workshop on Succinct Data Representations and Applications (Simons Institute Big Data 2013), Probability, Geometry, and Computation in High Dimensions Boot Camp (Simons Institute, Fall 2020), Algorithmic Advances for Statistical Inference with Combinatorial Structure]
as the organisers put it
This workshop will focus on recent developments in high-dimensional statistics, with an emphasis on different notions of robustness, the extent to which recent developments in theoretical computer science can lead to improvements with respect to traditional statistical metrics, challenges arising when the number of data points and the number of features diverge at similar rates, etc. Other potential topics are inference and causality, as well as inference after selection, i.e., data snooping and problems of multiple inference.
who it's for
high-dimensional statisticians, robust statistics researchers, machine learning researchers, theoretical computer scientists, optimization researchers, causal inference researchers, applied statisticians performing inference
topics
robust high-dimensional mean estimation; sum-of-squares algorithms for mixtures; outlier-robust linear regression; list decoding spherical Gaussians; hypothesis testing for weak signals; false discovery rate control methods; Tyler's M-estimator covariance thresholding; optimally weighted PCA for heteroscedastic data; orthogonal machine learning and K-orthogonality; TAP free energy and variational inference; stochastic proximal point versus SGD; anchor regression for causal robustness
| title | author | length |
|---|---|---|
| Robust List Decoding of Spherical Gaussians | Daniel Kane | 49m |
An algorithm uses multi-filters plus spectral checks and degree-d polynomial tests to list-decode a spherical Gaussian when only an alpha fraction of samples… | ||
| Computational-Statistical Tradeoffs in Robust High-Dimensional Estimation | Ilias Diakonikolas | 48m |
Shows that beating the current epsilon·sqrt(log(1/epsilon)) error for robust high‑dimensional Gaussian mean estimation forces either statistical query model… | ||
| Efficient Algorithms for Outlier-Robust Regression | Adam R. Klivans | 41m |
Provides a polynomial-time algorithm that tolerates an adversary corrupting an η fraction of training points and outputs a linear predictor whose square loss… | ||
| Detecting Weak Signals via Hypothesis Testing | Ravi Kannan | 39m |
Binary test between product noise P0 and a weak mixture signal (1−ε)P0+εP1 uses the chi‑square distance D = χ2(P1||P0) to set a sharp threshold: if ε√D → 0 no… | ||
| On Using Graph Distances to Estimate Euclidean and Related Distances | Ery Arias-Castro | 43m |
Uses graph shortest-path distances as proxies for unknown Euclidean or intrinsic (geodesic) distances and proves quantitative error bounds: when sample density… | ||
| The Importance of Better Models in Stochastic Optimization... | John Duchi | 47m |
Experiments compare stochastic gradient to stochastic proximal point and simple truncated models and claim proximal/truncated updates remain stable across… | ||
| Mixture Models, Robustness, and Sum of Squares Proofs | Jerry Li | 44m |
Gives an efficient pipeline using the Sum of Squares hierarchy to find bounded high-moment subsets and then recover parameters. For mixtures of K Gaussians… | ||
| Invariance, Causality and Novel Robustness | Peter Bühlmann | 44m |
Claim: causal regression coefficients are the minimizers of a worst‑case L2 risk over perturbations that do not act on Y, and a new estimator called anchor… | ||
| Generalization Bounds for Uniformly Stable Algorithms | Vitaly Feldman | 41m |
Shows a new high‑probability generalization bound for uniformly stable algorithms that replaces the prior γ·√n blowup with a bound that scales like √(γ + 1/n)… | ||
| Orthogonal Machine Learning: Power and Limitations | Lester Mackey | 44m |
Generalizes Neyman orthogonality to K-orthogonality and shows that if moment functions kill derivatives up to order K then nuisance estimators at rate… | ||
| Some Problems of Robust High-dimensional Statistics | Gilad Lerman | 44m |
Problem is robust subspace recovery with arbitrary adversarial outliers; adversary may place points anywhere and at any magnitude. Key claims: a RANSAC-type… | ||
| TAP Free Energy, Spin Glasses, and Variational Inference | Zhou Fan | 45m |
For the spiked Wigner model with ±1 prior, noise variance 1/N and signal strength λ (constant, λ>λ0), the usual product mean-field fails to approximate Bayes… | ||
| A Modern Maximum-Likelihood Theory for High-Dimensional Logistic Regression | Pragya Sur | 44m |
Claims that classical logistic MLE breaks down when p/n = κ is nonnegligible: coordinates concentrate around α·β_j (systematically inflated), their variance… | ||
| Robustness in High-Dimensional Inference Tasks | Jelena Bradic | 43m |
Claims a practical test for a single linear coefficient that works when the regression vector is dense, using an IV-style rewrite of the null and a constrained… | ||
| Controlling FDR While Highlighting Selected Discoveries | Chiara Sabatti | 48m |
Introduces focus BH, a small modification of Benjamini Hochberg that replaces the rejection count with the sum of data-driven weights Uj so FDR is controlled… | ||
| The Robustness of Controlling the False Discovery Rate | Weijie Su | 38m |
Shows that the Benjamini–Hochberg rule stays controlled under far weaker conditions than classical PRDS: any compliant procedure applied to null p‑values… | ||
| A Flexible Framework for Hypothesis Testing in High-Dimensions | Adel Javanmard | 36m |
Framework projects the high dimensional null onto a chosen K‑dimensional subspace then constructs a de‑biased estimator of U^T theta via a rotated debiasing… | ||
| Robust Sparse Covariance Estimation by Thresholding Tyler's M-estimator | Boaz Nadler | 48m |
Proposes that thresholded Tyler's M-estimator and its regularized variant recover an approximately sparse shape matrix for elliptical heavy‑tailed data at the… | ||
| Sub-Gaussian Mean Estimation in Polynomial Time | Samuel Hopkins | 45m |
Proposes a polynomial-time algorithm called median SDP that, after bucketing samples and using the median-of-means idea, finds a center whose confidence radius… | ||
| Robust Estimation and Generative Adversarial Nets | Chao Gao | 44m |
Works through Huber epsilon contamination and shows that depth estimators like Tukey's median and multi-task regression depths achieve exact minimax rates for… | ||
| Can Non-Convex Optimization be Robust? | Rong Ge | 46m |
Shows that if an unknown smooth objective F is pointwise close to an accessed function f with error nu ≤ O(ε^{3/2}/(√ρ · d)) then convolving f with a Gaussian… | ||
| Semi-Random Models and Robustness in Unsupervised Learning | Aravindan Vijayaraghavan | 45m |
A semi-random model mixes a tiny fraction beta of truly random sparse supports with adversarially chosen supports and shows polynomial-time recovery of the… | ||
| Optimally Weighted PCA for High-Dimensional Heteroscedastic Data | Laura Balzano | 40m |
Asymptotic analysis shows column-weighted PCA recovers a low-rank subspace better than unweighted PCA under heteroscedastic noise: with n,d → ∞ at fixed ratio… | ||
| How Many Directions Determine a Shape: A VC Theory for Modulii Spaces of Shapes | Sayan Mukherjee | 42m |
Proves that turning meshes into direction-wise topological summaries is information-preserving: the Euler characteristic transform and persistent homology… | ||
| Scale Calibration for High-Dimensional Robust Regression | Po-Ling Loh | 47m |
Proposes a practical pipeline that recovers sparse high-dimensional regression under heavy tails without knowing error scale: convex Huber+L1 initialization… | ||
| k-means and k-medians under Dimension Reduction | Yury Makarychev | 42m |
Shows that projecting by a random orthogonal or Gaussian map to dimension about d = Θ((log K)/ε^2) preserves the cost of every k‑means clustering up to 1+ε… | ||
| Efficient Profile Maximum Likelihood for Universal Symmetric Property Estimation | Moses Charikar | 45m |
Algorithm computes an approximate profile maximum likelihood distribution with objective value within a factor exp(O(N^{2/3})) of optimal, running in… | ||
| Realizing Robustness | Gautam Kamath | 31m |
Claim: efficient algorithms achieve O(ε) error for mean (and covariance) estimation under ε-corruption with no dimension-dependent factor; method: compute… | ||
| nothing matches | ||