New definition of joint stationarity improves process recovery over graphs.
problem Regression tasks with high-dimensional multivariate processes dependent on graph topology.
method Introduces joint stationarity, a new definition that reduces estimation variance and complexity.
result One reliably learns covariance structure from a single realization and solves MMSE problems nearly linearly in time.
This letter presents a novel Block Bayesian Hypothesis Testing Algorithm (Block-BHTA) for reconstructing block sparse signals with unknown block structures. The Block-BHTA comprises the detection and recovery of the supports, and the estimation of the amplitudes of the block sparse signal. The support detection and rec…
Paper proposes a neural network for sparse recovery using Laplace techniques.
problem Sparse recovery from compressed measurements.
method Designing a neural network to compute the centroid of a polytope.
result Analytical computation of volume and centroid enables efficient sparse recovery.
Risk-aware MMSE improves stability in volatile scenarios.
problem In MMSE estimators, volatility of error is unconstrained, leading to significant performance differences.
method Introduces risk-aware MMSE by constraining expected predictive variance.
result Risk-aware MMSE provides better performance, especially in skewed, heavy-tailed distributions.
A-MMSE uses attention to learn efficient OFDM channel estimation.
problem Accurate OFDM channel estimation requires second-order statistics, which are hard to obtain in practice.
method A-MMSE is a model-based DNN framework that learns linear MMSE filters via Attention Transformer, reducing inference complexity.
result A-MMSE outperforms other methods in normalized MSE across various SNR conditions.
AVICA estimates noise levels for better group ICA source recovery.
problem Estimating shared independent sources from multiple noisy views.
method AVICA models each view as a linear mixture of shared sources with additive noise, optimizing noise levels alongside sources.
result AVICA yields better source estimates than other methods, especially in real-world applications like MEG and fMRI.
Paper provides a new lower bound on MMSE using Poincaré inequality.
problem Estimating X from noisy Y in exponential family noise.
method Alternative MMSE representation + Poincaré inequality.
result New lower bound on MMSE holds for all distributions.
The study sets lower bounds on MMSE for inferring sensitive features from noisy data.
problem Estimating sensitive features from noisy observations of correlated features.
method Adversarial evaluation framework based on MMSE estimation with theoretical lower bounds.
result Derives closed-form bounds for linear models, showing optimality in noise variance.
New convergence rates found for PnP methods using MMSE denoisers.
problem Asymptotic convergence of PnP methods with MMSE denoisers.
method Explicitly represented MMSE denoiser as an upper Moreau envelope, derived sublinear convergence rates.
result First sublinear convergence guarantee for PnP proximal gradient descent with MMSE denoiser.
Paper finds formulas for mutual information and MMSE in matrix tensor product problems.
problem High-dimensional inference problems involving matrix tensor products.
method Single-letter formulas for mutual information and MMSE, using new techniques.
result Analytical formulas describe leading order terms in mutual information and MMSE.
Paper improves Fisher information estimation methods.
problem Estimating Fisher information for location parameters.
method Revisits and improves Bhattacharya estimator, introduces clipped estimator.
result Clipped estimator shows superior convergence rates in Gaussian noise.
This paper considers probabilistic estimation of a low-rank matrix from non-linear element-wise measurements of its elements. We derive the corresponding approximate message passing (AMP) algorithm and its state evolution. Relying on non-rigorous but standard assumptions motivated by statistical physics, we characteriz…
Study shows how much information can be learned from sparse signals with limited data.
problem Understanding information limits in learning sparse signals with sublinear data.
method Proved variational formula for mutual information, derived MMSE expressions, analyzed phase transitions.
result Nonincreasing piecewise constant MMSE with all-or-nothing phase transitions for certain conditions.
VAE leverages MMSE channel estimation with data-driven modeling.
problem Data-driven channel estimation for wireless communications.
method Variational autoencoder (VAE) modeling of channel distribution and LMMSE approximation.
result VAE-based channel estimators approximate MMSE performance with practical training methods.
Study finds exact limits for sparse regression with fewer observations than usual.
problem Understanding sparse linear regression with sublinear sparsity.
method Adaptive interpolation method and modified AMP algorithm.
result Exact asymptotic expressions for mutual information and MMSE in sublinear sparsity.
Paper proposes a blind predictor for unknown PSD Gaussian process.
problem Predicting a circular symmetric zero-mean stationary Gaussian process with unknown PSD.
method Random spectral representation and atomic-norm minimization for blind estimation.
result The proposed blind predictor performs comparably to an MMSE predictor with known PSD.
Algorithm predicts performance of learning in multi-layer networks with matrix-valued hidden variables.
problem Signal recovery and learning in multi-layer neural networks with matrix-valued hidden variables.
method Unified approximation algorithm for MAP and MMSE inference, extending ML-VAMP to handle matrix-valued unknowns.
result Performance of ML-Mat-VAMP algorithm can be predicted in a random large-system limit.
Paper establishes limits for accurately estimating low-rank matrices from noisy, non-linear data.
problem Estimating low-rank matrices from noisy, non-linear observations.
method Proves strong universality result with equivalent Gaussian model and effective prior parameters.
result Signal-to-noise ratio requirement grows as $N^{ rac 12 (1-1/k_F)}$ for accurate reconstruction.
Recently, a framework for application-oriented optimal experiment design has been introduced. In this context, the distance of the estimated system from the true one is measured in terms of a particular end-performance metric. This treatment leads to superior unknown system estimates to classical experiment designs bas…
End-to-end FCN framework optimizes speech enhancement metrics.
problem Inconsistency between model optimization and evaluation metrics.
method End-to-end utterance-based FCN for direct optimization of STOI.
result Enhanced speech has better STOI and improved intelligibility.
Study mutual info for community detection with covariate and correlated networks.
problem Community detection with covariate and correlated networks.
method Asymptotic upper bound and MMSE matrix heuristic analysis.
result Explicit characterization of combined information effects.
When recovering an unknown signal from noisy measurements, the computational difficulty of performing optimal Bayesian MMSE (minimum mean squared error) inference often necessitates the use of maximum a posteriori (MAP) inference, a special case of regularized M-estimation, as a surrogate. However, MAP is suboptimal in…
The most important aspect of any classifier is its error rate, because this quantifies its predictive capacity. Thus, the accuracy of error estimation is critical. Error estimation is problematic in small-sample classifier design because the error must be estimated using the same data from which the classifier has been…
Proposes variational autoencoder for efficient MMSE estimation.
problem Efficient parameterized MMSE estimation for noisy observations.
method Variational autoencoder models data distribution, approximates MMSE.
result Proposed estimator performs well compared to state-of-the-art.
Traditional Kalman filter (KF) is derived under the well-known minimum mean square error (MMSE) criterion, which is optimal under Gaussian assumption. However, when the signals are non-Gaussian, especially when the system is disturbed by some heavy-tailed impulsive noises, the performance of KF will deteriorate serious…
Paper proves L2 regression can learn k-juntas without distributional assumptions.
problem Learning k-juntas using L2 regression without distributional restrictions.
method L2 polynomial regression and minimum mean square estimation (MMSE).
result Agnostic PAC learning of k-juntas using L2 polynomial regression.
Paper introduces a new estimator for Rasch model with exact error analysis.
problem Estimating parameters of the Rasch model with performance guarantees.
method Develops a novel L-MMSE estimator for the Rasch model with nonasymptotic analysis.
result The L-MMSE estimator provides exact error analysis and performs similarly to state-of-the-art estimators.
Deep learning improves channel estimation in communication systems.
problem Improving channel estimation accuracy in communication systems.
method Proposed a deep learning pipeline using image processing techniques to estimate channel response.
result The proposed algorithm shows comparable performance to MMSE with full channel knowledge and better than ALMMSE.
Approximations of loopy belief propagation, including expectation propagation and approximate message passing, have attracted considerable attention for probabilistic inference problems. This paper proposes and analyzes a generalization of Opper and Winther's expectation consistent (EC) approximate inference method. Th…
Case vs control comparisons have been the classical approach to the study of neurological diseases. However, most patients will not fall cleanly into either group. Instead, clinicians will typically find patients that cannot be classified as having clearly progressed into the disease state. For those subjects, very lit…
ReQuestNet simplifies 5G channel estimation with a unified model.
problem Complex channel estimation in 5G systems with varying conditions.
method Unified neural architecture that handles dynamic resource blocks and transmit layers.
result Significantly outperforms legacy methods, achieving up to 10dB gain at high SNRs.
Convex penalty learning for optimal Bayesian signal estimation.
problem Optimizing signal estimation from noisy observations.
method Data-driven algorithm using ADMM and proximal mapping of convex penalty functions.
result Performance of the algorithm is practically identical to MMSE estimator.
Dual Bayesian Affine Estimators for Wiener-type state-space models
problem Estimating parameters in Wiener-type state-space models
method Fixed-point architecture combining two affine estimators
result Dual basis-parameter estimator achieves comparable parameter MSE to purely affine estimator
New model detects Alzheimer's and severity from speech, cognitive, and language data.
problem Detecting Alzheimer's disease and its severity from multimodal data.
method Multimodal ensemble system using acoustic, cognitive, and linguistic features.
result State-of-the-art accuracy and robustness in AD detection and MMSE score regression.
We derive an arbitrage free relationship between recovery swap rates, digital default swap spreads and conventional CDS spreads, and argue that the fair forward recovery rate used in recovery swaps must contain a convexity premium over the expected recovery value.
Develops algorithms for Bayesian inference with Plug & Play priors, ensuring convergence and well-posedness.
problem Bayesian imaging inverse problems with implicit priors defined by denoising algorithms.
method Introduces PnP-ULA and PnP-SGD algorithms for Monte Carlo sampling and MAP inference, proving convergence under realistic assumptions.
result Proves convergence of PnP-ULA and PnP-SGD algorithms for Bayesian inference with PnP priors, targeting a well-posed decision-theoretic model.
Method uses Seq2Seq learning to automatically generate recovery commands for ICT systems.
problem Manual decision-making for recovery commands is time-consuming and error-prone.
method Seq2Seq neural network model trained on past logs and commands.
result The model can estimate accurate recovery commands from new failures.
A new model explains U- and Swoosh-shaped stock price recovery during the COVID-19.
problem Modeling stock price recovery during the COVID-19 with V- and L-shaped recovery.
method Introducing a sentiment variable θ θ θ to quantify investor sentiment and simulate U- and Swoosh-shaped recovery. result The model explains U- and Swoosh-shaped recovery of sectoral indices with positive sentiment.
This paper improves support recovery in universal one-bit compressed sensing.
problem Support recovery in one-bit compressed sensing for sparse signals.
method Proposes approximate support recovery and superset recovery algorithms with polynomial-time complexity.
result Achieves improved support recovery with fewer measurements compared to existing methods.
Lower bounds on gradient queries for minimizing convex quadratic functions.
problem Proving lower bounds on the number of gradient queries needed to minimize convex quadratic functions.
method Careful reduction from adaptively estimating a planted vector in a deformed Wigner model.
result Lower bounds on the number of gradient queries required, showing Ω ( κ ) Ω(\sqrtκ) Ω ( κ ) for condition number κ κ κ . This work provides a guaranteed tensor recovery method by combining low-rankness and smoothness priors.
problem Guaranteed tensor recovery with theoretical guarantees for low-rank and smoothness priors.
method Developed a new regularization term that combines low-rankness and smoothness priors, proving exact recovery guarantees.
result Rigorously proved exact recovery guarantees for tensor completion and tensor robust principal component analysis.
This paper tackles tensor recovery from noisy and multi-level quantized measurements.
problem Tensors from multi-level quantized measurements.
method Nonconvex optimization problem with alternating proximal gradient descent.
result The recovery error diminishes to zero with increasing tensor dimensions.
We discuss a general notion of "sparsity structure" and associated recoveries of a sparse signal from its linear image of reduced dimension possibly corrupted with noise. Our approach allows for unified treatment of (a) the "usual sparsity" and "usual ℓ 1 \ell_1 ℓ 1 recovery," (b) block-sparsity with possibly overlapping blo…
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…
IRKSN algorithm achieves sparse recovery with wider applicability conditions.
problem Sparse recovery challenges due to NP-hard nature and restrictive conditions.
method IRKSN algorithm based on k k k -support norm regularizer. result Achieves sparse recovery with explicit constants and standard linear rate.
Enhances spoken speech quality using EEG signals.
problem Improves speech clarity in noisy environments.
method Generative adversarial network (GAN), gated recurrent unit (GRU), temporal convolutional network (TCN) regression models.
result Significant improvement in speech enhancement quality compared to traditional methods.
A framework for discrete structure recovery using iterative algorithms.
problem Recovering various discrete structures from data.
method General iterative algorithm for discrete structure recovery.
result Linear convergence of the proposed algorithm under certain conditions.
Study finds the cutoff for exact recovery in Gaussian mixture models.
problem Determining the separation of cluster centers for exact recovery in Gaussian mixture models.
method Used information theory and SDP relaxation of K K K -means clustering. result Sharp threshold for exact recovery of cluster labels without assuming cluster center symmetry.