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Found 40 papers, 0 papers with code
Agnostically Learning Multi-index Models with Queries
In contrast, algorithms that rely only on random examples inherently require $d^{\mathrm{poly}(1/\epsilon)}$ samples and runtime, even for the basic problem of agnostically learning a single ReLU or a halfspace.
Optimizing Solution-Samplers for Combinatorial Problems: The Landscape of Policy-Gradient Methods
Deep Neural Networks and Reinforcement Learning methods have empirically shown great promise in tackling challenging combinatorial problems.
Distribution-Independent Regression for Generalized Linear Models with Oblivious Corruptions
Our goal is to accurately recover a \new{parameter vector $w$ such that the} function $g(w \cdot x)$ \new{has} arbitrarily small error when compared to the true values $g(w^* \cdot x)$, rather than the noisy measurements $y$.
Self-Directed Linear Classification
In contrast, under a worst- or random-ordering, the number of mistakes must be at least $\Omega(d \log n)$, even when the points are drawn uniformly from the unit sphere and the learner only needs to predict the labels for $1\%$ of them.
Buying Information for Stochastic Optimization
In this paper, we study how to buy information for stochastic optimization and formulate this question as an online learning problem.
A Strongly Polynomial Algorithm for Approximate Forster Transforms and its Application to Halfspace Learning
By leveraging our strongly polynomial Forster algorithm, we obtain the first strongly polynomial time algorithm for {\em distribution-free} PAC learning of halfspaces.
Perfect Sampling from Pairwise Comparisons
We design a Markov chain whose stationary distribution coincides with $\mathcal{D}$ and give an algorithm to obtain exact samples using the technique of Coupling from the Past.
Learning a Single Neuron with Adversarial Label Noise via Gradient Descent
For the ReLU activation, we give an efficient algorithm with sample complexity $\tilde{O}(d\, \polylog(1/\epsilon))$.
Clustering with Queries under Semi-Random Noise
Our main result is a computationally efficient algorithm that can identify large clusters with $O\left(\frac{nk \log n} {(1-2p)^2}\right) + \text{poly}\left(\log n, k, \frac{1}{1-2p} \right)$ queries, matching the guarantees of the best known algorithms in the fully-random model.
Contextual Pandora's Box
Pandora's Box is a fundamental stochastic optimization problem, where the decision-maker must find a good alternative while minimizing the search cost of exploring the value of each alternative.
Online Learning for Min Sum Set Cover and Pandora's Box
In Pandora's Box, we are presented with $n$ boxes, each containing an unknown value and the goal is to open the boxes in some order to minimize the sum of the search cost and the smallest value found.
ReLU Regression with Massart Noise
This supervised learning task is efficiently solvable in the realizable setting, but is known to be computationally hard with adversarial label noise.
Approximating Pandora's Box with Correlations
For distributions of support $m$, UDT admits a $\log m$ approximation, and while a constant factor approximation in polynomial time is a long-standing open problem, constant factor approximations are achievable in subexponential time (arXiv:1906. 11385).
Efficient Algorithms for Learning from Coarse Labels
Our main algorithmic result is that essentially any problem learnable from fine grained labels can also be learned efficiently when the coarse data are sufficiently informative.
Learning General Halfspaces with General Massart Noise under the Gaussian Distribution
We study the general problem and establish the following: For $\eta <1/2$, we give a learning algorithm for general halfspaces with sample and computational complexity $d^{O_{\eta}(\log(1/\gamma))}\mathrm{poly}(1/\epsilon)$, where $\gamma =\max\{\epsilon, \min\{\mathbf{Pr}[f(\mathbf{x}) = 1], \mathbf{Pr}[f(\mathbf{x}) = -1]\} \}$ is the bias of the target halfspace $f$.
Forster Decomposition and Learning Halfspaces with Noise
A Forster transform is an operation that turns a distribution into one with good anti-concentration properties.
Boosting in the Presence of Massart Noise
Our upper and lower bounds characterize the complexity of boosting in the distribution-independent PAC model with Massart noise.
Agnostic Proper Learning of Halfspaces under Gaussian Marginals
We study the problem of agnostically learning halfspaces under the Gaussian distribution.
Convergence and Sample Complexity of SGD in GANs
Our main result is that by training the Generator together with a Discriminator according to the Stochastic Gradient Descent-Ascent iteration proposed by Goodfellow et al. yields a Generator distribution that approaches the target distribution of $f_*$.
Computationally and Statistically Efficient Truncated Regression
We provide a computationally and statistically efficient estimator for the classical problem of truncated linear regression, where the dependent variable $y = w^T x + \epsilon$ and its corresponding vector of covariates $x \in R^k$ are only revealed if the dependent variable falls in some subset $S \subseteq R$; otherwise the existence of the pair $(x, y)$ is hidden.
A Polynomial Time Algorithm for Learning Halfspaces with Tsybakov Noise
{\em We give the first polynomial-time algorithm for this fundamental learning problem.}
Efficient Parameter Estimation of Truncated Boolean Product Distributions
A stunning consequence is that virtually any statistical task (e. g., learning in total variation distance, parameter estimation, uniformity or identity testing) that can be performed efficiently for Boolean product distributions, can also be performed from truncated samples, with a small increase in sample complexity.
Learning Halfspaces with Tsybakov Noise
In the Tsybakov noise model, each label is independently flipped with some probability which is controlled by an adversary.
Non-Convex SGD Learns Halfspaces with Adversarial Label Noise
We study the problem of agnostically learning homogeneous halfspaces in the distribution-specific PAC model.
Black-box Methods for Restoring Monotonicity
In this work we develop algorithms that are able to restore monotonicity in the parameters of interest.
Learning Halfspaces with Massart Noise Under Structured Distributions
We study the problem of learning halfspaces with Massart noise in the distribution-specific PAC model.
On Robust Mean Estimation under Coordinate-level Corruption
We study the problem of robust mean estimation and introduce a novel Hamming distance-based measure of distribution shift for coordinate-level corruptions.
Efficient Truncated Statistics with Unknown Truncation
Our main result is a computationally and sample efficient algorithm for estimating the parameters of the Gaussian under arbitrary unknown truncation sets whose performance decays with a natural measure of complexity of the set, namely its Gaussian surface area.
Distribution-Independent PAC Learning of Halfspaces with Massart Noise
The goal is to find a hypothesis $h$ that minimizes the misclassification error $\mathbf{Pr}_{(\mathbf{x}, y) \sim \mathcal{D}} \left[ h(\mathbf{x}) \neq y \right]$.
Learning to Prune: Speeding up Repeated Computations
We present an algorithm that learns to maximally prune the search space on repeated computations, thereby reducing runtime while provably outputting the correct solution each period with high probability.
Efficient Statistics, in High Dimensions, from Truncated Samples
We provide an efficient algorithm for the classical problem, going back to Galton, Pearson, and Fisher, of estimating, with arbitrary accuracy the parameters of a multivariate normal distribution from truncated samples.
Anaconda: A Non-Adaptive Conditional Sampling Algorithm for Distribution Testing
This is an exponential improvement over the previous best upper bound, and demonstrates that the complexity of the problem in this model is intermediate to the the complexity of the problem in the standard sampling model and the adaptive conditional sampling model.
Actively Avoiding Nonsense in Generative Models
A generative model may generate utter nonsense when it is fit to maximize the likelihood of observed data.
Improving Viterbi is Hard: Better Runtimes Imply Faster Clique Algorithms
The classic algorithm of Viterbi computes the most likely path in a Hidden Markov Model (HMM) that results in a given sequence of observations.
A Converse to Banach's Fixed Point Theorem and its CLS Completeness
Our first result is a strong converse of Banach's theorem, showing that it is a universal analysis tool for establishing global convergence of iterative methods to unique fixed points, and for bounding their convergence rate.
Truthful Facility Location with Additive Errors
We address the problem of locating facilities on the $[0, 1]$ interval based on reports from strategic agents.
Ten Steps of EM Suffice for Mixtures of Two Gaussians
In the finite sample regime, we show that, under a random initialization, $\tilde{O}(d/\epsilon^2)$ samples suffice to compute the unknown vectors to within $\epsilon$ in Mahalanobis distance, where $d$ is the dimension.
Faster Sublinear Algorithms using Conditional Sampling
In contrast to prior algorithms for the classic model, our algorithms have time, space and sample complexity that is polynomial in the dimension and polylogarithmic in the number of points.
A Size-Free CLT for Poisson Multinomials and its Applications
Finally, leveraging the structural properties of the Fourier spectrum of PMDs we show that these distributions can be learned from $O_k(1/\varepsilon^2)$ samples in ${\rm poly}_k(1/\varepsilon)$-time, removing the quasi-polynomial dependence of the running time on $1/\varepsilon$ from the algorithm of Daskalakis, Kamath, and Tzamos.
On the Structure, Covering, and Learning of Poisson Multinomial Distributions
We prove a structural characterization of these distributions, showing that, for all $\varepsilon >0$, any $(n, k)$-Poisson multinomial random vector is $\varepsilon$-close, in total variation distance, to the sum of a discretized multidimensional Gaussian and an independent $(\text{poly}(k/\varepsilon), k)$-Poisson multinomial random vector.
