Study optimal portfolio selection with Recovery Average Value at Risk, showing better control over liabilities.
problem Optimizing portfolios with a new risk measure under known or uncertain distributions.
method Existence results for mean-risk optimal portfolios under different distributional assumptions.
result Portfolio selection under Recovery Average Value at Risk provides better control over liabilities.
Optimizes ranking of top-k players from partial comparison data.
problem Identifying the top-k players from incomplete pairwise comparisons.
method Maximum Likelihood Estimator (MLE) and Spectral Method.
result MLE achieves optimal partial and exact recovery, while Spectral Method is sub-optimal.
Paper reconciles minimax rates and optimal recovery rates for noisy observations.
problem Estimating a function from noisy observations.
method Develops NLA minimax rates for Besov classes in Lq-norms. result NLA minimax rates continuously depend on noise level and match optimal recovery rates as noise decreases.
Paper connects neural network hyperparameter optimization and NAS to structured sparse recovery.
problem Hyperparameter optimization and neural architecture search in neural networks.
method Structured sparse recovery methods applied to HPO and NAS.
result Improvements in hyperparameter optimization and discovery of novel neural architectures.
This paper advances FL algorithms for composite optimization and statistical recovery.
problem Federated learning optimization and statistical recovery in composite settings.
method Proposes Fast Federated Dual Averaging for strongly convex and smooth loss, and Multi-stage Federated Dual Averaging for restricted strongly convex and smooth loss.
result Establishes state-of-the-art iteration and communication complexity, and high probability complexity bound with linear speedup.
Optimal recovery framework for non-IID data in Hilbert spaces.
problem Generalization in non-IID data scenarios.
method Optimal recovery perspective, semidefinite programming, kernel ridgeless regression.
result Optimal recovery formula coincides with kernel ridgeless regression in some cases.
We consider the mixed regression problem with two components, under adversarial and stochastic noise. We give a convex optimization formulation that provably recovers the true solution, and provide upper bounds on the recovery errors for both arbitrary noise and stochastic noise settings. We also give matching minimax …
Efficient algorithm for robust recovery in stochastic block models.
problem Robust recovery in stochastic block models.
method Convex optimization framework, addressing optimization landscape challenges.
result Achieves robust recovery without a price of robustness.
Robust tensor recovery plays an instrumental role in robustifying tensor decompositions for multilinear data analysis against outliers, gross corruptions and missing values and has a diverse array of applications. In this paper, we study the problem of robust low-rank tensor recovery in a convex optimization framework,…
Improves graph recovery in Gaussian graphical modeling.
problem Calibrating regularization parameters for graph recovery.
method Thresholded adaptive validation applied to graphical lasso.
result Thresholding pipeline improves graph recovery.
Paper develops a new algorithm for sparse signal recovery.
problem Sparse signal recovery from noisy observations.
method Iterative Stochastic Optimization using Stochastic Mirror Descent.
result Linear convergence during preliminary phase of the routine.
We consider the problem of signal recovery on graphs as graphs model data with complex structure as signals on a graph. Graph signal recovery implies recovery of one or multiple smooth graph signals from noisy, corrupted, or incomplete measurements. We propose a graph signal model and formulate signal recovery as a cor…
New method recovers matrices with nonlinear structures using optimization on Grassmann manifold.
problem Recovering high-rank matrices with nonlinear structures like subspaces or clusters.
method Formulated as rank minimization of a nonlinear feature map, approximated by constrained non-convex optimization on the Grassmann manifold, using Riemannian and alternating minimization schemes.
result Global convergence and worst-case complexity bounds for alternating minimization scheme, leading to unique limit point.
New tensor recovery method uses Riemannian optimization on Segre manifold.
problem Recovering low-rank tensors from noisy measurements.
method Riemannian Gradient Descent (RGD) and Riemannian Gauss-Newton (RGN) algorithms over the Segre manifold.
result Proven convergence rates for RGD and RGN under mild noise assumptions.
Estimates spatio-temporal Hawkes processes using tensor recovery.
problem Estimating influence functions for spatio-temporal Hawkes processes.
method Formulates influence function as a tensor kernel, assumes low-rank structure, solves as convex optimization problem.
result Provides theoretical guarantees and demonstrates efficiency with simulations.
BalLOT uses optimal transport for balanced k-means clustering.
problem Balanced k-means clustering of data. method BalLOT is an optimal transport approach to alternating minimization.
result BalLOT provides theoretical guarantees for exact and partial recoveries of planted clusters.
Paper proposes efficient methods for clustering and signal recovery in high-dimensional data with block structures.
problem High-dimensional clustering and signal recovery under block signal structures.
method CFA-PCA and MA-PCA methods for sparse and dense block signals.
result Proposed methods achieve computational minimax optimality for clustering and signal recovery.
The paper tackles partial inference in structured prediction using a convex optimization approach.
problem Maximizing a score function with unary and pairwise potentials in graph label spaces.
method Generative model approach with two-stage convex optimization for label recovery.
result Conditions for recovering a majority of labels with provable guarantees.
Higher-order tensors can represent scores in a rating system, frames in a video, and images of the same subject. In practice, the measurements are often highly quantized due to the sampling strategies or the quality of devices. Existing works on tensor recovery have focused on data losses and random noises. Only a few …
This paper will serve as an introduction to the body of work on robust subspace recovery. Robust subspace recovery involves finding an underlying low-dimensional subspace in a dataset that is possibly corrupted with outliers. While this problem is easy to state, it has been difficult to develop optimal algorithms due t…
Study shows generative priors improve rank-one matrix recovery with optimal sample complexity.
problem Recovering a rank-one signal matrix from noisy data with additional prior information.
method Analysis of a nonlinear least squares objective with a favorable global optimization landscape.
result Established optimal sample complexity for generative priors in rank-one matrix recovery.
Study reveals efficient recovery of multi-modal signals via Bayesian methods and sequential learning.
problem Recovering multiple high-dimensional signals from correlated modalities.
method Bayesian Approximate Message Passing and Sequential Curriculum Learning.
result Sequential learning strategy optimally recovers weak signals in multi-modal settings.
Independent Component Analysis (ICA) is a popular model for blind signal separation. The ICA model assumes that a number of independent source signals are linearly mixed to form the observed signals. We propose a new algorithm, PEGI (for pseudo-Euclidean Gradient Iteration), for provable model recovery for ICA with Gau…
The problem of finding the sparsest vector (direction) in a low dimensional subspace can be considered as a homogeneous variant of the sparse recovery problem, which finds applications in robust subspace recovery, dictionary learning, sparse blind deconvolution, and many other problems in signal processing and machine …
Sharp threshold for exact recovery in non-uniform hypergraph stochastic block model.
problem Community detection in random hypergraphs with non-uniform hyperedge probabilities.
method Sharp threshold established; two efficient algorithms for exact recovery.
result Sharp threshold for exact recovery; information-theoretic lower bound on misclassification.
Our work is focused on the joint sparsity recovery problem where the common sparsity pattern is corrupted by Poisson noise. We formulate the confidence-constrained optimization problem in both least squares (LS) and maximum likelihood (ML) frameworks and study the conditions for perfect reconstruction of the original r…
New method improves dictionary recovery from over-realized models.
problem Theoretical guarantees for model recovery in dictionary learning are limited.
method Search over larger over-realized models to facilitate dictionary recovery.
result Model recovery can be upper-bounded by empirical risk and generalization gap.
New method tackles non-smooth tensor data for better recovery.
problem Non-smooth changes in tensor data degrade traditional t-SVD methods.
method Learnable tensor nuclear norm, Alternating Proximal Multiplier Method (APMM), multi-objective tensor recovery framework.
result The proposed method effectively recovers tensor data with non-smooth changes.
Exact recovery method for community detection in Gaussian mixtures with dependent noise.
problem Community detection in Gaussian mixtures with dependent and heterogeneous noise.
method Maximum likelihood estimator (MLE) for constrained quadratic optimization problem, using Σ-whitened separation and local inequalities. result Sharp exact-recovery threshold and no-gap mechanism in the unknown-size setting.
Binary Iterative Hard Thresholding converges with optimal number of 1-bit measurements.
problem Recovering sparse signals from 1-bit compressed measurements.
method Binary Iterative Hard Thresholding (BIHT) algorithm.
result BIHT converges with only O(k/ε) measurements, optimal for recovery.
New algorithm recovers matrices with unknown correspondences.
problem Recovering matrices from observations with unknown correspondences.
method Solves a nuclear norm minimization problem via proximal gradient with a Max-Oracle.
result Achieves state-of-the-art performance and high accuracy in recovering ground-truth correspondences.
Optimizes loan recovery timing by forecasting cash flows.
problem Minimizing overall credit loss in loan portfolios.
method Forecast future cash flows using probabilistic and Markov chain models.
result Empirical illustration of loss-optimal recovery timing.
Scaled gradient descent improves matrix recovery for ill-conditioned matrices with optimal sampling complexity.
problem Recovering low-rank matrices from limited measurements efficiently and accurately.
method Scaled gradient descent (ScaledGD) with optimal sample complexity and improved iteration complexity.
result ScaledGD achieves optimal sample complexity and improved iteration complexity for ill-conditioned matrices.
Posterior sampling estimator achieves near-optimal recovery guarantees for signals from any prior distribution.
problem Characterizing measurement complexity for signals from any prior distribution, including the entire space.
method Characterization of measurement complexity using posterior sampling estimator for Gaussian measurements and any prior distribution.
result Posterior sampling estimator achieves near-optimal recovery guarantees for signals from any prior distribution, robust to model mismatch.
New algorithm improves signal recovery from noisy measurements with theoretical guarantees.
problem Recovering signals from noisy measurements in inverse problems.
method Wasserstein-based projections (WP) replacing analytic regularization with data-driven denoising.
result WP approximates true projection with high probability, providing theoretical guarantees.
Optimal sparse recovery with decision stumps achieves strong feature selection guarantees.
problem Sparse recovery of active features from high-dimensional data.
method Analysis of single-depth decision trees (decision stumps) for feature selection in linear regression.
result Tight sample performance guarantees for O(slogp), improving upon previous bounds. Sparse matrices are favorable objects in machine learning and optimization. When such matrices are used, in place of dense ones, the overall complexity requirements in optimization can be significantly reduced in practice, both in terms of space and run-time. Prompted by this observation, we study a convex optimization…
Unified framework for pattern recovery in penalized and thresholded estimation.
problem Pattern recovery in penalized and thresholded estimation methods.
method Defining a novel pattern notion based on subdifferentials, introducing accessibility and noiseless recovery conditions.
result Unified and extended conditions for pattern recovery in a broad class of penalized estimators.
Small initialization improves tensor recovery from noisy data.
problem Recovering low-tubal-rank tensors from noisy measurements.
method Factorized gradient descent with small initialization.
result Achieves nearly minimax optimal recovery error.
This study optimizes multi-modal learning thresholds and algorithms in high dimensions.
problem Optimizing multi-modal learning performance in high-dimensional data.
method Analytical quantification and derivation of AMP algorithm with state evolution analysis.
result Bayes-optimal performance and recovery thresholds derived for multi-modal data.
We introduce a general framework to handle structured models (sparse and block-sparse with possibly overlapping blocks). We discuss new methods for their recovery from incomplete observation, corrupted with deterministic and stochastic noise, using block-ℓ1 regularization. While the current theory provides promis…
This paper investigates the problem of sparse signal recovery in the presence of additive impulsive noise. The heavytailed impulsive noise is well modelled with stable distributions. Since there is no explicit formulation for the probability density function of SαS distribution, alternative approximations like Genera…
In this paper we develop a novel computational sensing framework for sensing and recovering structured signals. When trained on a set of representative signals, our framework learns to take undersampled measurements and recover signals from them using a deep convolutional neural network. In other words, it learns a tra…
Nonconvex matrix recovery is known to contain no spurious local minima under a restricted isometry property (RIP) with a sufficiently small RIP constant δ. If δ is too large, however, then counterexamples containing spurious local minima are known to exist. In this paper, we introduce a proof technique that is capa…
Paper develops efficient AltMin algorithm for SRPCP robust matrix recovery.
problem SRPCP model robust matrix recovery with universal penalty parameter.
method Tuning-free alternating minimization (AltMin) algorithm with closed-form subproblems.
result Efficient AltMin algorithm confirms robustness and efficiency.
In this letter, we address sparse signal recovery using spike and slab priors. In particular, we focus on a Bayesian framework where sparsity is enforced on reconstruction coefficients via probabilistic priors. The optimization resulting from spike and slab prior maximization is known to be a hard non-convex problem, a…
Paper proposes a new method for exact recovery in robust tensor principal component analysis.
problem Exact recovery of low-rank and sparse components in tensors.
method Proposes a new method based on tensor-tensor product and t-SVD to solve a convex optimization problem.
result Exact recovery achieved in a deterministic fashion without randomness assumptions.
In this note we compare two recently proposed semidefinite relaxations for the sparse linear regression problem by Pilanci, Wainwright and El Ghaoui (Sparse learning via boolean relaxations, 2015) and Dong, Chen and Linderoth (Relaxation vs. Regularization A conic optimization perspective of statistical variable select…