Study on signal-plus-noise decomposition in nonlinear spiked random matrices.
problem Nonlinear spiked random matrix models with rank-one signal and noise.
method Signal-plus-noise decomposition and phase transition analysis.
result Identified precise phase transitions in signal components at critical thresholds.
Research compares ML and Time Series methods for generating trading signals.
problem Efficiency of on-line learning Algorithms in generating trading signals.
method Used technical indicators and ensemble of Random Forests, also Kalman Filter.
result Kalman Filter outperformed Random Forests in on-line learning predictions of stock prices.
SRMD uses random features for efficient time-frequency analysis.
problem Efficiently analyzing time-series data with low computational cost.
method Sparse Random Mode Decomposition (SRMD) constructs a sparse approximation to the spectrogram.
result SRMD outperforms other methods in signal representation, outlier removal, and mode decomposition.
The paper studies phase transitions in random matrices and tensor unfolding for detecting signals.
problem Phase transitions in singular values and vectors of large random matrices.
method Analysis of singular values and vectors of long rectangular random matrices, and tensor unfolding algorithm for asymmetric rank-one spiked tensor models.
result An exact threshold for tensor unfolding to detect signals, independent of unfolding procedure.
Data-driven methods link graphon limits to random walks and spectral clustering.
problem Clustering signals evolving over time with graphon limits.
method Transfer operators, Koopman and Perron-Frobenius, for estimating graphon from signal data.
result Spectral clustering can be extended to graphons, reconstructing transition densities and graphons.
It has been shown recently that graph signals with small total variation can be accurately recovered from only few samples if the sampling set satisfies a certain condition, referred to as the network nullspace property. Based on this recovery condition, we propose a sampling strategy for smooth graph signals based on …
Improves detection of low-rank signals from noisy data matrices.
problem Statistical detection of low-rank signals in noisy data matrices.
method Entrywise pre-transforming data matrix for non-Gaussian noise, sharp phase transition thresholds, central limit theorem for linear spectral statistics, hypothesis test.
result Improves detection of low-rank signals from noisy data matrices, generalizing known results.
The fields of compressed sensing (CS) and matrix completion have shown that high-dimensional signals with sparse or low-rank structure can be effectively projected into a low-dimensional space (for efficient acquisition or processing) when the projection operator achieves a stable embedding of the data by satisfying th…
New method shows random, diverse initializations are not essential for deep neural networks.
problem The necessity of random, diverse initializations in deep neural networks.
method Constructed a deep convolutional network with identical features by initializing weights to 0, enabling signal propagation and stable gradients.
result Random, diverse initializations are not necessary for training neural networks.
Proposes a probabilistic framework for stationary topological signals on simplicial complexes.
problem Complex data structures require new models and tools.
method Generalizes stationarity to topological signals on simplicial complexes.
result Defines topological power spectral density (PSD) for stationary signals.
Study detects signal in financial stock correlations using phase-ordering kinetics.
problem Detecting meaningful signals in financial stock return correlations.
method Stochastic field theory model to establish a detection threshold.
result Detection of a signal in the largest eigenvalues of the stock return correlation matrix.
Model classifies hand gestures with low EMG samples augmented with noise.
problem Classify hand gestures with limited EMG data.
method Random variance Gaussian noise augmentation, Random Forest, XGBoost.
result High accuracy model for six hand gestures.
Study uses random matrix theory to improve tensor approximation accuracy.
problem Improving tensor approximation accuracy in the presence of noise.
method Random matrix theory applied to tensor unfoldings.
result Characterizes spectral behavior of tensor unfoldings and predicts reconstruction performance.
We study signal recovery on graphs based on two sampling strategies: random sampling and experimentally designed sampling. We propose a new class of smooth graph signals, called approximately bandlimited, which generalizes the bandlimited class and is similar to the globally smooth class. We then propose two recovery s…
Paper improves privacy-preserving measurement of advertising incrementality.
problem Privacy degradation in randomized lift tests for advertising measurement.
method Formulates a robust causal decision problem under signal losses, projecting clean worlds onto incrementality.
result Sharp decision frontier shows valid certification or rejection outside the frontier.
Study reveals how attention helps in signal recovery from sequence models using random matrix theory.
problem Signal recovery from sequence models with attention mechanisms.
method Analysis of sample covariance matrices constructed from pooled sequence representations with attention weights.
result Optimal attention weights maximize signal-to-noise ratio and improve signal recovery.
Study analyzes perturbations in singular subspaces under random noise.
problem Understanding singular vector and subspace changes in signal-plus-noise models.
method Generalized Davis-Kahan-Wedin theorem for any unitarily invariant norm, considering ℓ∞ and ℓ2,∞ bounds. result Fine-grained insights into singular vector and subspace perturbations, including ℓ∞ and ℓ2,∞ bounds. This work improves structured prediction by learning the balance between signal and random noise.
problem Structured prediction with random perturbations.
method Learning the variance of randomized structured predictors to balance signal and noise.
result Learning the balance improves structured prediction effectiveness.
We study the problem of sampling a bandlimited graph signal in the presence of noise, where the objective is to select a node subset of prescribed cardinality that minimizes the signal reconstruction mean squared error (MSE). To that end, we formulate the task at hand as the minimization of MSE subject to binary constr…
Study analyzes Hotelling-type tensor deflation for spiked tensors, providing insights into signal and noise.
problem Characterizing singular values and alignments in Hotelling-type tensor deflation.
method Asymptotic study of Hotelling-type tensor deflation in large dimensional regime using random tensor theory.
result Characterization of singular values and alignments at each step of the deflation procedure.
This paper analyzes the interpolation error of nonlinear Attention compared to linear regression.
problem Understanding the interpolation error of nonlinear Attention in high-dimensional settings.
method Derives explicit expressions for mean-squared interpolation error using signal-plus-noise model and random matrix theory.
result Nonlinear Attention generally incurs a larger interpolation error than linear regression, but this gap can be reversed with structured signals.
Study on tensor signal estimation from incomplete data.
problem Estimating a rank-one tensor signal from noisy, incomplete data.
method Reduction to random matrix model for spectral analysis.
result Loss of performance due to incomplete data.
Better signal detection in undersampled data using joint and cross covariances.
problem Detecting shared signals in high-dimensional data with limited samples.
method Analysis of three covariance matrices: individual, cross, and joint.
result Joint and cross covariance matrices detect signals earlier than individual covariances.
We study the problem of sampling k-bandlimited signals on graphs. We propose two sampling strategies that consist in selecting a small subset of nodes at random. The first strategy is non-adaptive, i.e., independent of the graph structure, and its performance depends on a parameter called the graph coherence. On the co…
Bandlimited random neural networks may not approximate all functions perfectly.
problem Expressive power of shallow neural networks with bandlimited random weights.
method Ridgelet analysis for deriving approximation error lower bounds.
result Bandlimited random weights can lead to non-zero approximation error.
This study argues for pruning trees in random forests to improve performance in low signal-to-noise scenarios.
problem Improving random forest performance in scenarios with low signal-to-noise ratio.
method Using regularization theory, the study re-examines the depth of trees in random forests and provides evidence that shallow trees are advantageous.
result Random forests with shallow trees are advantageous when the signal-to-noise ratio is low.
Study evaluates thresholds for removing noise from DNN weights using random matrix theory.
problem Removing noise from deep neural network weights for better approximation.
method Model weights as signal + noise, use random matrix theory to estimate thresholds, evaluate using cosine similarity.
result Proposed threshold estimation method improves approximation quality.
The paper presents a method to recover high-resolution signals from low-resolution measurements.
problem Recovering high-resolution signals from low-resolution indirect measurements.
method Combining generalized sampling and functional principal component analysis.
result High-resolution recovery is possible under certain conditions and with a sufficiently large training set.
Study reveals limits of PLS in multi-modal learning with correlated signals.
problem Understanding PLS performance in multi-modal learning with correlated signals.
method Random matrix theory analysis of spiked cross-covariance models.
result Identifies SNR and correlation regimes where PLS fails to recover any signal.
SIMPLE-RC method tests group membership profiles in large networks with weak signals.
problem Testing group membership profiles in large networks with weak signals.
method Random coupling technique to construct maximum SIMPLE tests for subsampled node pairs.
result Asymptotic distributions of SIMPLE-RC test are derived, enabling delicate analysis.
Random matrix theory explains transient signal detectability in early-stopped gradient flow.
problem Transient signal detectability in early-stopped gradient flow.
method Random matrix theory applied to gradient flow in a linear teacher-student setting.
result Transient Baik-Ben Arous-Péché (BBP) transition in learning dynamics due to anisotropy and noise.
Study on detecting and recovering hidden dense cycles in random graphs.
problem Detecting and recovering hidden dense cycles in random graphs.
method Information-theoretic analysis of thresholds for detection and recovery.
result Characterization of information-theoretic thresholds for detection and recovery.
The paper improves classification accuracy by leveraging a shared signal across domains in high-dimensional classification.
problem Improving classification accuracy in high-dimensional data with shared signals across domains.
method Transfer learning for linear discriminant analysis, decomposing mean differences into common and domain-specific components.
result Deterministic limits for transfer performance, leading to optimal weights and corrections for bias.
Paper optimizes tensor deflation for non-orthogonal signals.
problem Recovering low-rank signals from noisy tensors with correlated components.
method Developed an asymptotic analysis and optimized deflation procedure using random tensor theory.
result Proposed an efficient tensor deflation algorithm that optimizes a parameter introduced in the deflation mechanism.
Paper proposes a new method combining random forests and Lasso selection.
problem Improving random forest performance by applying Lasso regression.
method Adaptive Lasso weighting applied to random forest predictions.
result Unified framework strictly outperforms other methods in simulations and real-world datasets.
U-Net trained to recover acoustic interference striations from distorted data.
problem Recovering acoustic interference striations from distorted signals.
method Training a U-Net using a random mode-coupling matrix model to generate training data.
result U-Net successfully recovers AISs under various conditions.
Alpha-trimming prunes trees in random forests to improve predictive performance.
problem Improving predictive performance of random forests by locally adaptive tree pruning.
method Alpha-trimming is a fast pruning algorithm that prunes trees in a random forest based on signal-to-noise ratio, controlled by a tuning parameter.
result Alpha-trimming often lowers mean squared prediction error compared to fully grown random forests.
This paper explores robust recovery of a superposition of R distinct complex exponential functions from a few random Gaussian projections. We assume that the signal of interest is of 2N−1 dimensional and R<<2N−1. This framework covers a large class of signals arising from real applications in biology, automation,…
Proposes a constrained labeling method for weakly supervised learning.
problem Combining weak supervision signals while navigating misleading correlations.
method Randomized constrained labeling within a defined space.
result Randomized constrained labeling converges after few iterations and outperforms other methods.
Neural networks are commonly trained to make predictions through learning algorithms. Contrastive Hebbian learning, which is a powerful rule inspired by gradient backpropagation, is based on Hebb's rule and the contrastive divergence algorithm. It operates in two phases, the forward (or free) phase, where the data are …
We extend the Deep Image Prior (DIP) framework to one-dimensional signals. DIP is using a randomly initialized convolutional neural network (CNN) to solve linear inverse problems by optimizing over weights to fit the observed measurements. Our main finding is that properly tuned one-dimensional convolutional architectu…
The bane of one-class collaborative filtering is interpreting and modelling the latent signal from the missing class. In this paper we present a novel Bayesian generative model for implicit collaborative filtering. It forms a core component of the Xbox Live architecture, and unlike previous approaches, delineates the o…
Spectral methods improve signal recovery in mixed GLMs with precise asymptotics.
problem Estimating multiple signals from unlabeled observations in mixed GLMs.
method Developed exact asymptotics for spectral methods in a proportional regime.
result Optimized spectral method combined with a linear estimator minimizes estimation error.
The paper proposes a method to improve random forest classification accuracy by weighting trees based on their decision path reliability.
problem Random forests' uniform voting fails to correct errors in regions where incorrect tree representations outnumber correct ones.
method The paper introduces using the structural pattern of each tree's decision path as an instance-adaptive reliability signal to identify and weight more reliable trees.
result Using the proposed method yields a statistically significant accuracy improvement over RF on 36 binary classification benchmarks.
Enhanced ELM reduces randomness in neural network training.
problem Challenges in ELM architecture design and sensitivity to random weight initialization.
method Introduces Effective Non-Random ELM (ENR-ELM) incorporating signal processing concepts.
result ENR-ELM simplifies architecture design and eliminates random weight selection.
A prototypical blind signal separation problem is the so-called cocktail party problem, with n people talking simultaneously and n different microphones within a room. The goal is to recover each speech signal from the microphone inputs. Mathematically this can be modeled by assuming that we are given samples from an n…
New estimator for tensor weights with improved bias.
problem Estimating tensor weights from noisy data.
method Random matrix theory and KKT conditions.
result Asymptotically unbiased estimator for tensor rank.
New method for identifying graph shift operators using vertex-time autoregressive models.
problem Identifying graph shift operators from graph signals.
method Online optimization using vertex-time autoregressive model and stochastic gradient projection.
result Successful recovery of graph shift operators from graph signals.