Local averaging accurately distills manifold structure from noisy data.
problem Tackles the challenge of uncovering manifold structure from noisy data.
method Two-round mini-batch local averaging method applied to noisy samples.
result Achieves accuracy bound of $d(\hat{\mathbf q}, \mathcal M) \leq σ\sqrt{d\left(1+\frac{κ\mathrm{diam}(\mathcal {M})}{\log(D)}
ight)}$ .
K-means fails in high dimensions with noise and few samples.
problem Clustering in high-dimensional data with noise and limited samples.
method Simple Gaussian Mixture Model (GMM) analysis.
result Almost every partition becomes a fixed point of k-means in high dimensions.
Neural networks parameterize time-varying Markov dynamics in financial time series.
problem Estimating Markov transition matrices in high-resolution, high-noise financial data.
method Introduces a neural network framework to generate explicit, time-varying Markov transition matrices, constraining neural outputs to formal stochastic operators.
result Learned operators capture regime shifts, with high-volatility regimes homogenizing transition dynamics.
We study a seemingly unexpected and relatively less understood overfitting aspect of a fundamental tool in sparse linear modeling - best subset selection, which minimizes the residual sum of squares subject to a constraint on the number of nonzero coefficients. While the best subset selection procedure is often perceiv…
This work optimizes signal estimation for sparse MRA with collision-free signals.
problem Recovering an unknown signal from repeated observations under cyclic isometries with high noise.
method Investigates minimax optimality for collision-free signals in the MRA model.
result The minimax optimal rate of estimation is \( \sigma^2/\sqrt{n} \) for sparse MRA.
New findings show privacy affects generalization error in a non-monotonic way.
problem Privacy and robustness in distributed learning.
method Theoretical analysis and matching lower/upper bounds on algorithmic stability.
result Generalization error is non-monotonically affected by privacy, depending on noise level.
We present a new method for the separation of superimposed, independent, auto-correlated components from noisy multi-channel measurement. The presented method simultaneously reconstructs and separates the components, taking all channels into account and thereby increases the effective signal-to-noise ratio considerably…
New method uses neural networks for accurate angle estimation in noisy conditions.
problem Accurately estimate angles from noisy measurements in various applications.
method Directed Graph Neural Networks (GNNSync) for end-to-end trainable framework.
result GNNSync achieves competitive performance, even at high noise levels.
Minimal DAMs can recognize patterns in high noise, even with minimal data.
problem Pattern recognition in high noise conditions with limited data.
method Interpolating between DAMs and spin glasses, using minimal dense associative networks and extremizing quenched free-energy.
result Minimal DAMs can correctly recognize patterns even when the signal is very weak and noise is high.
This work establishes distribution-free upper and lower bounds on the minimax label complexity of active learning with general hypothesis classes, under various noise models. The results reveal a number of surprising facts. In particular, under the noise model of Tsybakov (2004), the minimax label complexity of active …
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.
Improved SGD with AdaGrad stepsizes adapts to unknown parameters and unbounded gradients.
problem Adaptive optimization with unknown parameters and unbounded gradients.
method Stochastic Gradient Descent with AdaGrad stepsizes, without assuming problem parameters or strong global Lipschitz conditions.
result Sharp rates of convergence in both low-noise and high-noise regimes, supporting an affine variance noise model.
A method for estimating parameters from entangled single-sample distributions, robust to high-noise data.
problem Estimating common parameters from entangled single-sample distributions.
method Iterative trimming of samples to estimate the parameter.
result The method can tolerate a constant fraction of high-noise data points.
SoftBart improves BART for high-noise modeling in science.
problem High noise in scientific data.
method Soft BART algorithm for Bayesian additive regression trees.
result Improves predictive performance and facilitates larger model integration.
We analyze anomaly detection class imbalance using a solvable model.
problem Class imbalance hampers anomaly detection performance.
method We use an exact solution of the teacher-student perceptron model through replica theory.
result Optimal train imbalance is often different from 50%, influenced by intrinsic imbalance and data abundance.
RAD improves robustness to domain annotation noise without explicit domain annotations.
problem Robustness to domain annotation noise in training data.
method Regularized Annotation of Domains (RAD) for last layer retraining.
result RAD outperforms state-of-the-art methods even with 5% noise in training data.
New algorithm learns permutations mixtures with optimal sample complexity.
problem Learning mixtures of permutations in high-dimensional settings.
method Combining groups of pairwise comparisons and combinatorial method of moments.
result Optimal sample complexity proportional to log(n) for high-dimensional data.
Enhances weak lensing inference with neural summaries.
problem Extracting additional information from weak lensing convergence maps.
method Hybrid approach combining physics-based and neural summaries.
result Neural summaries extract up to 8 times more information than angular power spectra.
Developing efficient and guaranteed nonconvex algorithms has been an important challenge in modern machine learning. Algorithms with good empirical performance such as stochastic gradient descent often lack theoretical guarantees. In this paper, we analyze the class of homotopy or continuation methods for global optimi…
SPPCSO addresses multicollinearity in high-dimensional data, improving model stability and predictive accuracy.
problem Multicollinearity in high-dimensional data leads to unstable estimation and reduced predictive accuracy.
method SPPCSO integrates principal component regression and L1 regularization to adaptively adjust shrinkage factors.
result SPPCSO achieves stable and reliable estimation in high-noise settings, distinguishing signal variables from noise.
Bayesian autoencoders discover physics from noisy data.
problem Challenges in identifying governing equations and coordinates from noisy, low-data real-world data.
method Bayesian SINDy autoencoders with hierarchical Bayesian sparsifying prior and adaptive empirical Bayesian method.
result Better physics discovery with lower data and fewer training epochs, along with valid uncertainty quantification.
New framework uses score-based priors to solve ill-conditioned polynomial equations, improving signal recovery from noisy data.
problem Recovering signals from low-order moments in inverse problems, especially ill-conditioned polynomial equations.
method Integrates score-based diffusion priors with moment-based estimators to regularize and solve nonlinear inverse problems.
result Diffusion priors improve recovery from third-order moments and make super-resolution MTD feasible.
Deep learning improves model discovery from sparse sensor data.
problem Improving physical understanding and predictions from coarse, non-grid sampled data.
method Physics-informed neural networks and automatic differentiation.
result Deep learning can recover underlying equations from sparse, non-grid data.
A new method selects features for clustering without labels.
problem Identifying meaningful features in large datasets.
method Differentiable unsupervised feature selection using a gated Laplacian.
result The method improves clustering performance in noisy data.
Data-driven discovery of differential equations has been an emerging research topic. We propose a novel algorithm subsampling-based threshold sparse Bayesian regression (SubTSBR) to tackle high noise and outliers. The subsampling technique is used for improving the accuracy of the Bayesian learning algorithm. It has tw…
A method merges two pretrained diffusion experts to improve image quality and likelihood.
problem Trade-off between image quality and data likelihood in diffusion models.
method Combining two pretrained diffusion experts by switching between them along the denoising trajectory.
result The merged model consistently matches or outperforms its base components, improving or preserving both likelihood and sample quality.
New findings show sparse signals in MRA model require fewer measurements than previously thought.
problem Learning an unknown signal from repeated noisy images under group actions.
method Enhanced probabilistic method and analysis of uniform uncertainty principles.
result Sparse signals exhibit intermediate σ 4 σ^4 σ 4 sample complexity, improving over traditional σ 2 σ^2 σ 2 . Bayesian framework detects symmetries in chaotic dynamical systems.
problem Detecting symmetries in chaotic attractors for insights into dynamical system structure.
method Bayesian framework using Gibbs posterior constructed from Wasserstein distances.
result Bayesian framework accurately recovers symmetries under high noise and small sample sizes.
Two new methods reduce random forest latency and improve accuracy.
problem High latency and memory demands in deep random forest models.
method DiNo and RanBu convert shallow random forests into efficient predictors.
result RanBu matches or exceeds full-depth random forest accuracy with up to 95% reduction in time.
Hybrid quantum-classical model boosts S&P 500 prediction accuracy to 60.14%.
problem Challenges in financial market prediction, especially high noise and non-stationarity.
method Combines quantum sentiment analysis, Decision Transformer, and model selection strategies.
result Achieved 60.14% directional accuracy on S&P 500, a 3.10% improvement.
Differentiable clustering method using perturbed spanning forests.
problem Efficient clustering in trainable pipelines with noisy data.
method Stochastic perturbations of minimum-weight spanning forests.
result Method performs well even in challenging settings.
A new random forest algorithm uncovers feature interdependencies better than traditional methods.
problem Tackles the sub-optimality of greedy decision tree implementations in random forests.
method Presented a 'stepwise lookahead' variation of random forests that considers multiple split nodes simultaneously.
result Significantly outperforms greedy random forests in uncovering feature interdependencies, especially in high-noise environments.
Cross-regularization adapts model complexity during training.
problem Manual tuning of model complexity for overfitting prevention.
method Directly adapts regularization parameters through validation gradients during training.
result Organic emergence of architecture-specific regularization during training.
New EiV models correct bias in operator learning with noisy data.
problem Bias in operator learning due to noisy independent variables.
method Developed EiV models for MOR-Physics and DeepONet.
result EiV models reduce bias in noisy operator learning.
Frequency estimation is a fundamental problem in signal processing, with applications in radar imaging, underwater acoustics, seismic imaging, and spectroscopy. The goal is to estimate the frequency of each component in a multisinusoidal signal from a finite number of noisy samples. A recent machine-learning approach u…
K-means fails catastrophically in high dimensions, Hartigan's avoids it.
problem K-means algorithm's failure in high-dimensional data.
method Proof of k-means failure and Hartigan's algorithm success.
result Hartigan's algorithm avoids the catastrophic failure of k-means in high dimensions.
Paper tackles noisy bandit feedback for multiclass classification.
problem Learning multiclass classifier with corrupted feedback.
method Proposes an unbiased estimator technique to estimate noise rates and an end-to-end framework.
result Algorithm achieves mistake bounds of O ( T ) O(\sqrt{T}) O ( T ) in high noise and O ( T i c e f r a c 23 ) O(T^{
icefrac{2}{3}}) O ( T i ce f r a c 2 3 ) in worst case. The article detects market regimes from covariance matrices using VLSTAR and clustering models.
problem Market regime switching is hard to detect due to time-varying correlation coefficients.
method The article applies VLSTAR and unsupervised hierarchical clustering on monthly realized covariance matrices.
result VLSTAR outperforms clustering in detecting market regimes.
The study identifies and analyzes different market regimes in equity markets using advanced signal processing techniques.
problem Understanding and quantifying the dynamics of different market regimes in equity markets.
method Data-driven Hilbert--Huang Transform for regime identification, Holo--Hilbert Spectral Analysis for profiling, and Variable-Length Markov Chains for return dynamics modeling.
result Developed markets normalize more effectively as stress subsides, while developing markets retain residual tail dependence and downside persistence.
In Machine Learning, ensemble methods have been receiving a great deal of attention. Techniques such as Bagging and Boosting have been successfully applied to a variety of problems. Nevertheless, such techniques are still susceptible to the effects of noise and outliers in the training data. We propose a new method for…
Paper improves asset allocation using machine learning for regime detection.
problem Improving asset allocation strategies in uncertain economic conditions.
method Machine learning for regime detection, modified k-means algorithm, portfolio optimization.
result Significant portfolio performance improvements over traditional benchmarks.
Improved image quality in diffusion models by limiting guidance to a specific noise level range.
problem Improving image quality in diffusion models with guidance.
method Restricting guidance to a specific noise level range.
result Significantly improved FID score from 1.81 to 1.40 in ImageNet-512.
New bounds quantify estimation error in kernel-based system identification with unknown hyperparameters.
problem Inaccurate error bounds for kernel-based system identification with unknown hyperparameters.
method Construct a high-probability set for true hyperparameters from marginal likelihood, then find worst-case posterior covariance.
result Proposed bounds contain true model with high probability and verified in simulations.
Proposes methods for learning optimal dynamic treatment regimes robust to unconfoundedness violations.
problem Estimating optimal dynamic treatment regimes using historical observational data when unconfoundedness is violated.
method Utilizes proximal causal inference framework to propose three nonparametric identification methods, a (K+1)-robust method, and establish a semiparametric efficiency bound.
result Establishes the (K+1)-robust method for learning optimal dynamic treatment regimes, validating its efficiency and multiple robustness through numerical experiments.
New model identifies regimes in non-stationary data.
problem Identifying latent regimes in non-stationary systems with instantaneous effects.
method Identifiable Markov Switching Models with exponential family noise.
result Established identifiability of latent regimes and causal structures.
Markov regime switching models have been used in numerous empirical studies in economics and finance. However, the asymptotic distribution of the likelihood ratio test statistic for testing the number of regimes in Markov regime switching models has been an unresolved problem. This paper derives the asymptotic distribu…
Algorithm classifies market regimes using time series signatures.
problem Classifying different market conditions from time series data.
method Utilizes path signatures and a metric structure for clustering.
result Established a connection between regime separation and point clustering.
RegimeFolio optimizes portfolios by adapting to changing market regimes.
problem Non-stationary markets with shifting volatility regimes.
method Explicitly models volatility regimes with sector-specific ensemble forecasting and adaptive mean-variance allocation.
result Significant improvement in return and robustness compared to conventional methods.