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Found 40 papers, 5 papers with code
Sampling from the Mean-Field Stationary Distribution
We study the complexity of sampling from the stationary distribution of a mean-field SDE, or equivalently, the complexity of minimizing a functional over the space of probability measures which includes an interaction term.
Beyond Labeling Oracles: What does it mean to steal ML models?
We discover that prior knowledge of the attacker, i. e. access to in-distribution data, dominates other factors like the attack policy the adversary follows to choose which queries to make to the victim model API.
Distributional Model Equivalence for Risk-Sensitive Reinforcement Learning
We consider the problem of learning models for risk-sensitive reinforcement learning.
Distributional Reinforcement Learning
reinforcement-learning
Towards a Complete Analysis of Langevin Monte Carlo: Beyond Poincaré Inequality
We do so by establishing upper and lower bounds for Langevin diffusions and LMC under weak Poincar\'e inequalities that are satisfied by a large class of densities including polynomially-decaying heavy-tailed densities (i. e., Cauchy-type).
Mean-Square Analysis of Discretized Itô Diffusions for Heavy-tailed Sampling
We analyze the complexity of sampling from a class of heavy-tailed distributions by discretizing a natural class of It\^o diffusions associated with weighted Poincar\'e inequalities.
Improved Discretization Analysis for Underdamped Langevin Monte Carlo
As a byproduct, we also obtain the first KL divergence guarantees for ULMC without Hessian smoothness under strong log-concavity, which is based on a new result on the log-Sobolev constant along the underdamped Langevin diffusion.
Neural Networks Efficiently Learn Low-Dimensional Representations with SGD
We further demonstrate that, SGD-trained ReLU NNs can learn a single-index target of the form $y=f(\langle\boldsymbol{u},\boldsymbol{x}\rangle) + \epsilon$ by recovering the principal direction, with a sample complexity linear in $d$ (up to log factors), where $f$ is a monotonic function with at most polynomial growth, and $\epsilon$ is the noise.
Generalization Bounds for Stochastic Gradient Descent via Localized $\varepsilon$-Covers
In this paper, we propose a new covering technique localized for the trajectories of SGD.
$p$-DkNN: Out-of-Distribution Detection Through Statistical Testing of Deep Representations
We introduce $p$-DkNN, a novel inference procedure that takes a trained deep neural network and analyzes the similarity structures of its intermediate hidden representations to compute $p$-values associated with the end-to-end model prediction.
High-dimensional Asymptotics of Feature Learning: How One Gradient Step Improves the Representation
We study the first gradient descent step on the first-layer parameters $\boldsymbol{W}$ in a two-layer neural network: $f(\boldsymbol{x}) = \frac{1}{\sqrt{N}}\boldsymbol{a}^\top\sigma(\boldsymbol{W}^\top\boldsymbol{x})$, where $\boldsymbol{W}\in\mathbb{R}^{d\times N}, \boldsymbol{a}\in\mathbb{R}^{N}$ are randomly initialized, and the training objective is the empirical MSE loss: $\frac{1}{n}\sum_{i=1}^n (f(\boldsymbol{x}_i)-y_i)^2$.
Mirror Descent Strikes Again: Optimal Stochastic Convex Optimization under Infinite Noise Variance
We study stochastic convex optimization under infinite noise variance.
Towards a Theory of Non-Log-Concave Sampling: First-Order Stationarity Guarantees for Langevin Monte Carlo
For the task of sampling from a density $\pi \propto \exp(-V)$ on $\mathbb{R}^d$, where $V$ is possibly non-convex but $L$-gradient Lipschitz, we prove that averaged Langevin Monte Carlo outputs a sample with $\varepsilon$-relative Fisher information after $O( L^2 d^2/\varepsilon^2)$ iterations.
Heavy-tailed Sampling via Transformed Unadjusted Langevin Algorithm
We analyze the oracle complexity of sampling from polynomially decaying heavy-tailed target densities based on running the Unadjusted Langevin Algorithm on certain transformed versions of the target density.
Analysis of Langevin Monte Carlo from Poincaré to Log-Sobolev
Classically, the continuous-time Langevin diffusion converges exponentially fast to its stationary distribution $\pi$ under the sole assumption that $\pi$ satisfies a Poincar\'e inequality.
Convergence and Optimality of Policy Gradient Methods in Weakly Smooth Settings
Policy gradient methods have been frequently applied to problems in control and reinforcement learning with great success, yet existing convergence analysis still relies on non-intuitive, impractical and often opaque conditions.
On Empirical Risk Minimization with Dependent and Heavy-Tailed Data
In this work, we establish risk bounds for the Empirical Risk Minimization (ERM) with both dependent and heavy-tailed data-generating processes.
Fractal Structure and Generalization Properties of Stochastic Optimization Algorithms
As our main contribution, we prove that the generalization error of a stochastic optimization algorithm can be bounded based on the `complexity' of the fractal structure that underlies its invariant measure.
Heavy Tails in SGD and Compressibility of Overparametrized Neural Networks
Neural network compression techniques have become increasingly popular as they can drastically reduce the storage and computation requirements for very large networks.
Manipulating SGD with Data Ordering Attacks
Machine learning is vulnerable to a wide variety of attacks.
Convergence Rates of Stochastic Gradient Descent under Infinite Noise Variance
In this paper, we provide convergence guarantees for SGD under a state-dependent and heavy-tailed noise with a potentially infinite variance, for a class of strongly convex objectives.
On the Ergodicity, Bias and Asymptotic Normality of Randomized Midpoint Sampling Method
The randomized midpoint method, proposed by [SL19], has emerged as an optimal discretization procedure for simulating the continuous time Langevin diffusions.
Riemannian Langevin Algorithm for Solving Semidefinite Programs
We propose a Langevin diffusion-based algorithm for non-convex optimization and sampling on a product manifold of spheres.
Convergence of Langevin Monte Carlo in Chi-Squared and Renyi Divergence
We prove that, initialized with a Gaussian random vector that has sufficiently small variance, iterating the LMC algorithm for $\widetilde{\mathcal{O}}(\lambda^2 d\epsilon^{-1})$ steps is sufficient to reach $\epsilon$-neighborhood of the target in both Chi-squared and Renyi divergence, where $\lambda$ is the logarithmic Sobolev constant of $\nu_*$.
Hausdorff Dimension, Heavy Tails, and Generalization in Neural Networks
Despite its success in a wide range of applications, characterizing the generalization properties of stochastic gradient descent (SGD) in non-convex deep learning problems is still an important challenge.
An Analysis of Constant Step Size SGD in the Non-convex Regime: Asymptotic Normality and Bias
Structured non-convex learning problems, for which critical points have favorable statistical properties, arise frequently in statistical machine learning.
On the Convergence of Langevin Monte Carlo: The Interplay between Tail Growth and Smoothness
This convergence rate, in terms of $\epsilon$ dependency, is not directly influenced by the tail growth rate $\alpha$ of the potential function as long as its growth is at least linear, and it only relies on the order of smoothness $\beta$.
Towards Characterizing the High-dimensional Bias of Kernel-based Particle Inference Algorithms
Particle-based inference algorithm is a promising method to efficiently generate samples for an intractable target distribution by iteratively updating a set of particles.
Stochastic Runge-Kutta Accelerates Langevin Monte Carlo and Beyond
In this paper, we establish the convergence rate of sampling algorithms obtained by discretizing smooth It\^o diffusions exhibiting fast Wasserstein-$2$ contraction, based on local deviation properties of the integration scheme.
Normal Approximation for Stochastic Gradient Descent via Non-Asymptotic Rates of Martingale CLT
A crucial intermediate step is proving a non-asymptotic martingale central limit theorem (CLT), i. e., establishing the rates of convergence of a multivariate martingale difference sequence to a normal random vector, which might be of independent interest.
Global Non-convex Optimization with Discretized Diffusions
An Euler discretization of the Langevin diffusion is known to converge to the global minimizers of certain convex and non-convex optimization problems.
Convergence Rate of Block-Coordinate Maximization Burer-Monteiro Method for Solving Large SDPs
Furthermore, incorporating Lanczos method to the block-coordinate maximization, we propose an algorithm that is guaranteed to return a solution that provides $1-O(1/r)$ approximation to the original SDP without any assumptions, where $r$ is the rank of the factorization.
Robust Estimation of Neural Signals in Calcium Imaging
We use our proposed robust loss in a matrix factorization framework to extract the neurons and their temporal activity in calcium imaging datasets.
Inference in Graphical Models via Semidefinite Programming Hierarchies
We demonstrate that the resulting algorithm can solve problems with tens of thousands of variables within minutes, and outperforms BP and GBP on practical problems such as image denoising and Ising spin glasses.
Scaled Least Squares Estimator for GLMs in Large-Scale Problems
We study the problem of efficiently estimating the coefficients of generalized linear models (GLMs) in the large-scale setting where the number of observations $n$ is much larger than the number of predictors $p$, i. e. $n\gg p \gg 1$.
Scalable Approximations for Generalized Linear Problems
Using this relation, we design an algorithm that achieves the same accuracy as the empirical risk minimizer through iterations that attain up to a cubic convergence rate, and that are cheaper than any batch optimization algorithm by at least a factor of $\mathcal{O}(p)$.
Newton-Stein Method: A Second Order Method for GLMs via Stein's Lemma
We consider the problem of efficiently computing the maximum likelihood estimator in Generalized Linear Models (GLMs)when the number of observations is much larger than the number of coefficients (n > > p > > 1).
Newton-Stein Method: An optimization method for GLMs via Stein's Lemma
We consider the problem of efficiently computing the maximum likelihood estimator in Generalized Linear Models (GLMs) when the number of observations is much larger than the number of coefficients ($n \gg p \gg 1$).
Convergence rates of sub-sampled Newton methods
In this regime, algorithms which utilize sub-sampling techniques are known to be effective.
SEISMIC: A Self-Exciting Point Process Model for Predicting Tweet Popularity
Social networking websites allow users to create and share content.
Social and Information Networks Physics and Society Applications 60G55, 62P25 H.2.8
Estimating LASSO Risk and Noise Level
In this context, we develop new estimators for the $\ell_2$ estimation risk $\|\hat{\theta}-\theta_0\|_2$ and the variance of the noise.
