arXiv research

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

Noiseless KRR achieves optimal rates and exhibits saturation effects.

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

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

Noiseless IO bounds inferred from demonstrations, matching adversarial settings.

Unified framework for pattern recovery in penalized and thresholded estimation.

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

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

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…

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…

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

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…

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 algorithm learns permutations mixtures with optimal sample complexity.

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…

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.

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

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 …

NOMU improves neural network uncertainty estimation.

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 …

In the problem of learning mixtures of linear regressions, the goal is to learn a collection of signal vectors from a sequence of (possibly noisy) linear measurements, where each measurement is evaluated on an unknown signal drawn uniformly from this collection. This setting is quite expressive and has been studied bot…

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…

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

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

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

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

Parallel Bayesian optimization tackles noisy multi-objective problems.

The multivariate linear regression model with shuffled data and additive Gaussian noise arises in various correspondence estimation and matching problems. Focusing on the denoising aspect of this problem, we provide a characterization the minimax error rate that is sharp up to logarithmic factors. We also analyze the p…

We study the problem of inferring a sparse vector from random linear combinations of its components. We propose the Accelerated Orthogonal Least-Squares (AOLS) algorithm that improves performance of the well-known Orthogonal Least-Squares (OLS) algorithm while requiring significantly lower computational costs. While OL…

We propose a general framework for reconstructing and denoising single entries of incomplete and noisy entries. We describe: effective algorithms for deciding if and entry can be reconstructed and, if so, for reconstructing and denoising it; and a priori bounds on the error of each entry, individually. In the noiseless…

New method calculates Shapley values for uncertain functions.

We consider the classical sparse regression problem of recovering a sparse signal $x_0$ given a measurement vector $y = Φx_0+w$. We propose a tree search algorithm driven by the deep neural network for sparse regression (TSN). TSN improves the signal reconstruction performance of the deep neural network designed for sp…

Analyzing historical data of price indices we find an extraordinary growth phenomenon in several examples of hyper-inflation in which price changes are approximated nicely by double-exponential functions of time. In order to explain such behavior we introduce the general coarse-graining technique in physics, the Monte …

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…

The paper addresses rigid alignment of noisy patches, providing a polynomial time algorithm and convergence conditions.

Improved PINNs for solving PDEs with unknown measurement noise.

Quantum computing improves fill probability estimation in bond trading.

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…

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 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 algorithms reduce communication costs in collaborative learning.

Low-rank signal modeling has been widely leveraged to capture non-local correlation in image processing applications. We propose a new method that employs low-rank tensor factor analysis for tensors generated by grouped image patches. The low-rank tensors are fed into the alternative direction multiplier method (ADMM) …

In this paper, we propose a general framework for sparse and low-rank tensor estimation from cubic sketchings. A two-stage non-convex implementation is developed based on sparse tensor decomposition and thresholded gradient descent, which ensures exact recovery in the noiseless case and stable recovery in the noisy cas…