Any width-m two-layer piecewise-linear network with arbitrary weights that fits n noisy labels below the noise floor has Lip ≳ ε sqrt(n/(m log(m n d/ε))) with high probability on the sphere or Gaussian.
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Thomas Hofmann, Bernhard Sch¨ olkopf, and Alexander J Smola
23 Pith papers cite this work, alongside 1,505 external citations. Polarity classification is still indexing.
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Local privacy mechanisms preserve rate-double-robustness, enabling unbiased and semiparametrically efficient inference on target parameters indexed linearly by infinite-dimensional and nonlinearly by low-dimensional components from noisy private data.
By folding normalization into a KL-based objective over un-normalized potentials, neural likelihood approximation becomes a strictly convex problem with provable consistency.
Direct fixed-weight solver for free-support Wasserstein medians relocates atoms using OT barycentric projections and inverse-distance weights, achieving monotone descent on smoothed objectives with fewer subproblems than nested Weiszfeld baselines.
Establishes optimal dimension-free sampling complexities (k²/ε² for L2/k, k/ε² for L1/k, linear in k under bounded derivative) for regularized classification losses with matching lower bounds.
A linked Tucker tensor factorization enables a joint individualized hurdle-ordinal regression model that uncovers spatially heterogeneous effects of fluoride and diet on paired caries and fluorosis outcomes.
Improved upper bounds on the number of loci required for a bipartition cover under the multispecies coalescent, obtained by worst-case analysis of caterpillar and balanced species trees.
An R package that unifies spatio-temporal STARMA and GARCH-type models through double generalized linear models, allowing simultaneous modeling of means and dispersion for count or continuous spatial time series.
Heat-kernel smoothing over weighted points on a compact manifold yields a scale-dependent geometric effective sample size that discounts nearby and duplicate particles.
First-order Edgeworth expansions with O(n^{-1}) remainders are established for general linear rank statistics via Stein's method and an extension of Bolthausen's combinatorial method.
A cycle-counting-ratio estimator for the β-model achieves minimax-optimal MSE and consistency under the weak conditions θ_max→0 and θ_t‖θ‖₁→∞, even at network densities near log n/n.
Anchor PCA recovers a maximal invariant subspace for multi-domain data via PCA on a modified target matrix that trades off explained variance with domain agreement.
New discrete-time approximations to SG(L)D enable accurate non-asymptotic predictions of covariance and integrated autocorrelation time for practical tuning in large-batch or misspecified regimes.
The nonparametric Kiefer-Weiss problem is solved by deriving an optimal stopping policy based on a two-dimensional statistic (likelihood ratio plus expected remaining sample size) whose randomization rule maps the likelihood ratio to an integer sample size.
Planet-hosting stars display a bimodal S_phot distribution (peaks at 0.12 and 0.44 rad d^{-1}) absent in controls, with overall enhancement, interpreted as two regimes of magnetic activity coherence.
A public catalogue provides geometric and photogeometric distances plus uncertainties for 1.47 billion Gaia EDR3 stars derived via probabilistic inference with a three-dimensional Galactic prior.
New asymptotically pivotal and identification-robust nonparametric tests for parameters in linear IV models handling unknown heteroskedasticity.
A review reframing density estimation as 'density evolution' across scales, linking kernel smoothing to heat flow, mixtures to compression, and topology to level sets, while stating three structural results on modes, Gaussian semigroups, and log-concavity.
SPICE is a scalable Bayesian MCMC engine for explanatory IRT calibration on sparsely linked persons and items in large assessment banks.
critband delivers the first cohesive Python implementation of Silverman's critical bandwidth bimodality test with k-mode detection, component decomposition, and benchmarked performance gains over R's modetest.
Develops and compares consistent estimators for gradual change points in nonparametric regression using a new optimization method targeting the largest minimization point of an objective function, with rates, regression estimation, bootstrap, and two-sample extensions.
Review and simulation comparison of more than 40 threshold selection procedures for univariate extreme value analysis, with application to daily rainfall data.
Plasmoid reconnection simulations match observed skewness transitions and entropy decreases in FSRQ GeV light curves after flares, with broken power-law PSDs consistent with blazar variability.
citing papers explorer
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A law of robustness for two-layer neural networks with arbitrary weights
Any width-m two-layer piecewise-linear network with arbitrary weights that fits n noisy labels below the noise floor has Lip ≳ ε sqrt(n/(m log(m n d/ε))) with high probability on the sphere or Gaussian.
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Private Rate-Double-Robust Inference
Local privacy mechanisms preserve rate-double-robustness, enabling unbiased and semiparametrically efficient inference on target parameters indexed linearly by infinite-dimensional and nonlinearly by low-dimensional components from noisy private data.
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A Convex Approximation Framework for Neural Likelihood-Based Bayesian Inverse Problems
By folding normalization into a KL-based objective over un-normalized potentials, neural likelihood approximation becomes a strictly convex problem with provable consistency.
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Fast Computation of Free-Support Wasserstein Medians
Direct fixed-weight solver for free-support Wasserstein medians relocates atoms using OT barycentric projections and inverse-distance weights, achieving monotone descent on smoothed objectives with fewer subproblems than nested Weiszfeld baselines.
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Optimal Dimension-Free Sampling for Regularized Classification
Establishes optimal dimension-free sampling complexities (k²/ε² for L2/k, k/ε² for L1/k, linear in k under bounded derivative) for regularized classification losses with matching lower bounds.
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Linked-Tucker Factorized Individualized Regression for Paired Multivariate Categorical Outcomes
A linked Tucker tensor factorization enables a joint individualized hurdle-ordinal regression model that uncovers spatially heterogeneous effects of fluoride and diet on paired caries and fluorosis outcomes.
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An Improved Bipartition Cover Bound for the Multispecies Coalescent Model
Improved upper bounds on the number of loci required for a bipartition cover under the multispecies coalescent, obtained by worst-case analysis of caterpillar and balanced species trees.
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glmSTARMA -- An R-Package for fitting autoregressive spatio-temporal models following generalized linear models
An R package that unifies spatio-temporal STARMA and GARCH-type models through double generalized linear models, allowing simultaneous modeling of means and dispersion for count or continuous spatial time series.
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Heat-Kernel Entropy Profiles and Geometric Effective Sample Size for Weighted Measures on Manifolds
Heat-kernel smoothing over weighted points on a compact manifold yields a scale-dependent geometric effective sample size that discounts nearby and duplicate particles.
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Edgeworth Expansions for Linear Rank Statistics -- Consolidated Version
First-order Edgeworth expansions with O(n^{-1}) remainders are established for general linear rank statistics via Stein's method and an extension of Bolthausen's combinatorial method.
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Subgraph counting estimation for the $\beta$-model in sparse networks
A cycle-counting-ratio estimator for the β-model achieves minimax-optimal MSE and consistency under the weak conditions θ_max→0 and θ_t‖θ‖₁→∞, even at network densities near log n/n.
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Anchor PCA
Anchor PCA recovers a maximal invariant subspace for multi-domain data via PCA on a modified target matrix that trades off explained variance with domain agreement.
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Accurate Large-sample Uncertainty Quantification using Stochastic Gradient Markov Chain Monte Carlo
New discrete-time approximations to SG(L)D enable accurate non-asymptotic predictions of covariance and integrated autocorrelation time for practical tuning in large-batch or misspecified regimes.
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The Nonparametric Kiefer-Weiss Problem
The nonparametric Kiefer-Weiss problem is solved by deriving an optimal stopping policy based on a two-dimensional statistic (likelihood ratio plus expected remaining sample size) whose randomization rule maps the likelihood ratio to an integer sample size.
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Bimodality in Rotational Modulation of Planet-Hosting Stars
Planet-hosting stars display a bimodal S_phot distribution (peaks at 0.12 and 0.44 rad d^{-1}) absent in controls, with overall enhancement, interpreted as two regimes of magnetic activity coherence.
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Estimating distances from parallaxes. V: Geometric and photogeometric distances to 1.47 billion stars in Gaia Early Data Release 3
A public catalogue provides geometric and photogeometric distances plus uncertainties for 1.47 billion Gaia EDR3 stars derived via probabilistic inference with a three-dimensional Galactic prior.
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Pivotal and identification-robust nonparametric inference in linear IV models
New asymptotically pivotal and identification-robust nonparametric tests for parameters in linear IV models handling unknown heteroskedasticity.
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Density Evolution: A Multiscale View of Density Estimation
A review reframing density estimation as 'density evolution' across scales, linking kernel smoothing to heat flow, mixtures to compression, and topology to level sets, while stating three structural results on modes, Gaussian semigroups, and log-concavity.
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A Scalable Parametric Item Calibration Engine (SPICE) for Explanatory IRT with Sparse Data
SPICE is a scalable Bayesian MCMC engine for explanatory IRT calibration on sparsely linked persons and items in large assessment banks.
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critband: A Python Package for Critical Bandwidth Analysis of Multimodal Distributions
critband delivers the first cohesive Python implementation of Silverman's critical bandwidth bimodality test with k-mode detection, component decomposition, and benchmarked performance gains over R's modetest.
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Analysis of gradual changes in nonparametric regression based on a new optimization method in the non-unique case
Develops and compares consistent estimators for gradual change points in nonparametric regression using a new optimization method targeting the largest minimization point of an objective function, with rates, regression estimation, bootstrap, and two-sample extensions.
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Choosing the threshold in extreme value analysis
Review and simulation comparison of more than 40 threshold selection procedures for univariate extreme value analysis, with application to daily rainfall data.
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Reconnection-driven State Transitions in Flat Spectrum Radio Quasars
Plasmoid reconnection simulations match observed skewness transitions and entropy decreases in FSRQ GeV light curves after flares, with broken power-law PSDs consistent with blazar variability.