arXiv research

Stochastic gradient descent achieves polynomial convergence rates for noiseless linear models.

Noiseless KRR achieves optimal rates and exhibits saturation effects.

The study examines Kernel Ridge Regression error rates across noiseless and noisy conditions.

Study shows efficient algorithms for noiseless linear regression require quadratic sample complexity in contamination rate.

Paper improves learning mixtures of sparse signals from noisy measurements.

Noiseless IO bounds inferred from demonstrations, matching adversarial settings.

Modern deep neural network models suffer from adversarial examples, i.e. confidently misclassified points in the input space. It has been shown that Bayesian neural networks are a promising approach for detecting adversarial points, but careful analysis is problematic due to the complexity of these models. Recently Gil…

New algorithm learns permutations mixtures with optimal sample complexity.

Unified framework for pattern recovery in penalized and thresholded estimation.

Tensor CANDECOMP/PARAFAC (CP) decomposition is an important tool that solves a wide class of machine learning problems. Existing popular approaches recover components one by one, not necessarily in the order of larger components first. Recently developed simultaneous power method obtains only a high probability recover…

Improved GP bandit algorithms for noiseless, varying noise, and RKHS norms.

Recently developed deep-learning-based denoisers often outperform state-of-the-art conventional denoisers such as the BM3D. They are typically trained to minimize the mean squared error (MSE) between the output image of a deep neural network (DNN) and a ground truth image. Thus, it is important for deep-learning-based …

Paper solves graph matching problem using convex relaxation to the simplex.

This paper considers compressed sensing and affine rank minimization in both noiseless and noisy cases and establishes sharp restricted isometry conditions for sparse signal and low-rank matrix recovery. The analysis relies on a key technical tool which represents points in a polytope by convex combinations of sparse v…

In a noiseless linear estimation problem, one aims to reconstruct a vector x* from the knowledge of its linear projections y=Phi x*. There have been many theoretical works concentrating on the case where the matrix Phi is a random i.i.d. one, but a number of heuristic evidence suggests that many of these results are un…

We provide high-probability sample complexity guarantees for exact structure recovery and accurate predictive learning using noise-corrupted samples from an acyclic (tree-shaped) graphical model. The hidden variables follow a tree-structured Ising model distribution, whereas the observable variables are generated by a …

This paper introduces SRPR for robust phase retrieval with smoothed loss functions.

The paper sets sample complexity bounds for learning high-dimensional simplices in noisy data.

Paper introduces a neural network training algorithm for noisy data that achieves optimal parameters and replicates real-world behaviors.

We propose a unified framework for estimating low-rank matrices through nonconvex optimization based on gradient descent algorithm. Our framework is quite general and can be applied to both noisy and noiseless observations. In the general case with noisy observations, we show that our algorithm is guaranteed to linearl…

We study the problem of robust subspace recovery (RSR) in the presence of adversarial outliers. That is, we seek a subspace that contains a large portion of a dataset when some fraction of the data points are arbitrarily corrupted. We first examine a theoretical estimator that is intractable to calculate and use it to …

New algorithms reduce communication costs in collaborative learning.

In active learning, the user sequentially chooses values for feature $X$ and an oracle returns the corresponding label $Y$. In this paper, we consider the effect of feature noise in active learning, which could arise either because $X$ itself is being measured, or it is corrupted in transmission to the oracle, or the o…

Deep neural networks can generalize well even with perfect fits to noisy data.

This paper studies continuum-armed bandits under Besov smoothness conditions and derives minimax rates.

We study the problem of estimating low-rank matrices from linear measurements (a.k.a., matrix sensing) through nonconvex optimization. We propose an efficient stochastic variance reduced gradient descent algorithm to solve a nonconvex optimization problem of matrix sensing. Our algorithm is applicable to both noisy and…

New method calculates Shapley values for uncertain functions.

In this paper we model the problem of learning preferences of a population as an active learning problem. We propose an algorithm can adaptively choose pairs of items to show to users coming from a heterogeneous population, and use the obtained reward to decide which pair of items to show next. We provide computational…

Quantum computing improves fill probability estimation in bond trading.

We analyze random feature and two-layer neural networks using duality framework.

Among the plethora of techniques devised to curb the prevalence of noise in medical images, deep learning based approaches have shown the most promise. However, one critical limitation of these deep learning based denoisers is the requirement of high-quality noiseless ground truth images that are difficult to obtain in…

We consider the problem of learning classifiers for labeled data that has been distributed across several nodes. Our goal is to find a single classifier, with small approximation error, across all datasets while minimizing the communication between nodes. This setting models real-world communication bottlenecks in the …

Efficiently generates noiseless samples from noisy data using manifold hypothesis.

The homology groups of a manifold are important topological invariants that provide an algebraic summary of the manifold. These groups contain rich topological information, for instance, about the connected components, holes, tunnels and sometimes the dimension of the manifold. In earlier work, we have considered the s…

This paper resolves BIHT convergence, showing normalization is not necessary in noiseless settings but crucial for robustness.

Paper analyzes EM algorithm's trajectory in 2MLR, revealing cycloid behavior.

Deep neural networks achieve optimal learning rates for high-dimensional classification.

This work precisely characterizes and improves the tradeoff between robustness and accuracy in linear regression.

Algorithm learns decision trees from noisy data.

Parallel Bayesian optimization tackles noisy multi-objective problems.

Improved PINNs for solving PDEs with unknown measurement noise.

We study the sample complexity of learning a high-dimensional simplex from a set of points uniformly sampled from its interior. Learning of simplices is a long studied problem in computer science and has applications in computational biology and remote sensing, mostly under the name of `spectral unmixing'. We theoretic…

We present the Tamed Cross Entropy (TCE) loss function, a robust derivative of the standard Cross Entropy (CE) loss used in deep learning for classification tasks. However, unlike other robust losses, the TCE loss is designed to exhibit the same training properties than the CE loss in noiseless scenarios. Therefore, th…

New method bounds hardware noise without assumptions.

NOMU improves neural network uncertainty estimation.

The study examines denoising and noisy-input regression under distribution shift, revealing double descent behavior and insights for data augmentation.

Adversarial training can hurt robust accuracy in small sample size scenarios.

We propose a method for zeroth order stochastic convex optimization that attains the suboptimality rate of $\tilde{\mathcal{O}}(n^{7}T^{-1/2})$ after $T$ queries for a convex bounded function $f:{\mathbb R}^n\to{\mathbb R}$. The method is based on a random walk (the \emph{Ball Walk}) on the epigraph of the function. Th…