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Found 42 papers, 3 papers with code
Distribution Estimation under the Infinity Norm
A variety of techniques are utilized and innovated upon, including Chernoff-type inequalities and empirical Bernstein bounds.
Splitting the Difference on Adversarial Training
The ability to achieve such near-optimal natural accuracy, while maintaining a significant level of robustness, makes our method applicable to real-world applications where natural accuracy is at a premium.
Efficient Agnostic Learning with Average Smoothness
While the recent work of Hanneke et al. (2023) established tight uniform convergence bounds for average-smooth functions in the realizable case and provided a computationally efficient realizable learning algorithm, both of these results currently lack analogs in the general agnostic (i. e. noisy) case.
Differentially-Private Bayes Consistency
We construct a universally Bayes consistent learning rule that satisfies differential privacy (DP).
Metric-valued regression
We propose an efficient algorithm for learning mappings between two metric spaces, $\X$ and $\Y$.
Adaptive Data Analysis with Correlated Observations
The vast majority of the work on adaptive data analysis focuses on the case where the samples in the dataset are independent.
Tree density estimation
data we identify an optimal tree $T^*$ and efficiently construct a tree density estimate $f_n$ such that, without any regularity conditions on the density $f$, one has $\lim_{n\to \infty} \int |f_n(\boldsymbol x)-f_{T^*}(\boldsymbol x)|d\boldsymbol x=0$ a. s. For Lipschitz $f$ with bounded support, $\mathbb E \left\{ \int |f_n(\boldsymbol x)-f_{T^*}(\boldsymbol x)|d\boldsymbol x\right\}=O\big(n^{-1/4}\big)$, a dimension-free rate.
Fat-Shattering Dimension of $k$-fold Aggregations
We provide estimates on the fat-shattering dimension of aggregation rules of real-valued function classes.
Domain Invariant Adversarial Learning
We present a new adversarial training method, Domain Invariant Adversarial Learning (DIAL), which learns a feature representation that is both robust and domain invariant.
Stable Sample Compression Schemes: New Applications and an Optimal SVM Margin Bound
We analyze a family of supervised learning algorithms based on sample compression schemes that are stable, in the sense that removing points from the training set which were not selected for the compression set does not alter the resulting classifier.
Non-parametric Binary regression in metric spaces with KL loss
We propose a non-parametric variant of binary regression, where the hypothesis is regularized to be a Lipschitz function taking a metric space to [0, 1] and the loss is logarithmic.
Functions with average smoothness: structure, algorithms, and learning
Rather than using the Lipschitz constant as the regularizer, we define a local slope at each point and gauge the function complexity as the average of these values.
On Biased Random Walks, Corrupted Intervals, and Learning Under Adversarial Design
We tackle some fundamental problems in probability theory on corrupted random processes on the integer line.
Nested Barycentric Coordinate System as an Explicit Feature Map
We propose a new embedding method which is particularly well-suited for settings where the sample size greatly exceeds the ambient dimension.
Apportioned Margin Approach for Cost Sensitive Large Margin Classifiers
We consider the problem of cost sensitive multiclass classification, where we would like to increase the sensitivity of an important class at the expense of a less important one.
Fast and Bayes-consistent nearest neighbors
Research on nearest-neighbor methods tends to focus somewhat dichotomously either on the statistical or the computational aspects -- either on, say, Bayes consistency and rates of convergence or on techniques for speeding up the proximity search.
Universal Bayes consistency in metric spaces
This is the first learning algorithm known to enjoy this property; by comparison, the $k$-NN classifier and its variants are not generally universally Bayes-consistent, except under additional structural assumptions, such as an inner product, a norm, finite dimension, or a Besicovitch-type property.
Efficient Kirszbraun Extension with Applications to Regression
We introduce a framework for performing regression between two Hilbert spaces.
Estimating the Mixing Time of Ergodic Markov Chains
Furthermore, even if an eigenvalue perturbation analysis with better dependence on $d$ were available, in the non-reversible case the connection between the spectral gap and the mixing time is not nearly as straightforward as in the reversible case.
Minimax Testing of Identity to a Reference Ergodic Markov Chain
We exhibit an efficient procedure for testing, based on a single long state sequence, whether an unknown Markov chain is identical to or $\varepsilon$-far from a given reference chain.
Improved Generalization Bounds for Adversarially Robust Learning
For binary classification, the algorithm of Feige et al. (2015) uses a regret minimization algorithm and an ERM oracle as a black box; we adapt it for the multiclass and regression settings.
Agnostic Sample Compression Schemes for Regression
For the $\ell_2$ loss, does every function class admit an approximate compression scheme of polynomial size in the fat-shattering dimension?
Statistical Estimation of Ergodic Markov Chain Kernel over Discrete State Space
We investigate the statistical complexity of estimating the parameters of a discrete-state Markov chain kernel from a single long sequence of state observations.
Learning convex polyhedra with margin
We present an improved algorithm for {\em quasi-properly} learning convex polyhedra in the realizable PAC setting from data with a margin.
Sample Compression for Real-Valued Learners
We give an algorithmically efficient version of the learner-to-compression scheme conversion in Moran and Yehudayoff (2016).
A New Lower Bound for Agnostic Learning with Sample Compression Schemes
We establish a tight characterization of the worst-case rates for the excess risk of agnostic learning with sample compression schemes and for uniform convergence for agnostic sample compression schemes.
Mixing time estimation in reversible Markov chains from a single sample path
The interval is constructed around the relaxation time $t_{\text{relax}} = 1/\gamma$, which is strongly related to the mixing time, and the width of the interval converges to zero roughly at a $1/\sqrt{n}$ rate, where $n$ is the length of the sample path.
Temporal anomaly detection: calibrating the surprise
We learn a low-rank stationary model from the training data, and then fit a regression model for predicting the expected likelihood score of normal access patterns in the future.
Nearest-Neighbor Sample Compression: Efficiency, Consistency, Infinite Dimensions
We examine the Bayes-consistency of a recently proposed 1-nearest-neighbor-based multiclass learning algorithm.
Exact Lower Bounds for the Agnostic Probably-Approximately-Correct (PAC) Machine Learning Model
Based on this result, an exact asymptotic lower bound on the minimax EER is provided.
Active Nearest-Neighbor Learning in Metric Spaces
We propose a pool-based non-parametric active learning algorithm for general metric spaces, called MArgin Regularized Metric Active Nearest Neighbor (MARMANN), which outputs a nearest-neighbor classifier.
Mixing Time Estimation in Reversible Markov Chains from a Single Sample Path
The interval is constructed around the relaxation time $t_{\text{relax}}$, which is strongly related to the mixing time, and the width of the interval converges to zero roughly at a $\sqrt{n}$ rate, where $n$ is the length of the sample path.
Nearly optimal classification for semimetrics
We initiate the rigorous study of classification in semimetric spaces, which are point sets with a distance function that is non-negative and symmetric, but need not satisfy the triangle inequality.
A Bayes consistent 1-NN classifier
We show that a simple modification of the 1-nearest neighbor classifier yields a strongly Bayes consistent learner.
Near-optimal sample compression for nearest neighbors
We present the first sample compression algorithm for nearest neighbors with non-trivial performance guarantees.
Maximum Margin Multiclass Nearest Neighbors
We prove generalization bounds that match the state of the art in sample size $n$ and significantly improve the dependence on the number of classes $k$.
Consistency of weighted majority votes
We revisit the classical decision-theoretic problem of weighted expert voting from a statistical learning perspective.
Predictive PAC Learning and Process Decompositions
We informally call a stochastic process learnable if it admits a generalization error approaching zero in probability for any concept class with finite VC-dimension (IID processes are the simplest example).
Concentration in unbounded metric spaces and algorithmic stability
We prove an extension of McDiarmid's inequality for metric spaces with unbounded diameter.
Efficient Classification for Metric Data
We design a new algorithm for classification in general metric spaces, whose runtime and accuracy depend on the doubling dimension of the data points, and can thus achieve superior classification performance in many common scenarios.
Adaptive Metric Dimensionality Reduction
We study adaptive data-dependent dimensionality reduction in the context of supervised learning in general metric spaces.
Efficient Regression in Metric Spaces via Approximate Lipschitz Extension
We present a framework for performing efficient regression in general metric spaces.
