Machine learning predicts Kronecker coefficients with high accuracy.
problem Predicting Kronecker coefficients from tensor products of symmetric group representations.
method Training machine learning models (NN, CNN, GBDT) to classify Kronecker coefficients as zero or non-zero.
result Trained models achieve high accuracy (≈0.98) in classifying Kronecker coefficients. Paper proposes methods for transfer learning with random coefficient ridge regression.
problem Estimation and prediction in high-dimensional settings with related models.
method Two estimators using weighted sums of ridge estimates from target and source models.
result Explicit expression of estimation and prediction risks derived using random matrix theory.
Framework uses deep learning and statistical models to solve PDEs with discontinuous coefficients.
problem Solving PDEs with discontinuous coefficients.
method Two-stage physics-informed deep learning and statistical mixture models.
result Framework achieves adaptability and accurate parameter identification.
The study predicts Kronecker coefficients using interpretable machine learning models.
problem Predicting Kronecker coefficients of the symmetric group.
method Employed interpretable machine learning models with input features of triples of partitions and b-loadings.
result Achieved an accuracy of approximately 83% and over 99% with transformer-based models.
A new method estimates the learning coefficient using empirical loss.
problem Estimating the learning coefficient in complex models.
method Numerical estimation using Empirical Loss.
result Our method outperforms existing techniques in terms of bias and variance.
Estimates LLC for deep linear networks up to 100M parameters.
problem Quantifying model complexity for large-scale deep learning architectures.
method Empirical estimation of LLC using a method developed for DLNs.
result LLC can be accurately measured for DLNs up to 100M parameters.
Proposes an adversarial algorithm to learn unbiased representations via HGR coefficient.
problem Learning fair representations without sensitive attribute information.
method Adversarial algorithm using Hirschfeld-Gebelein-Renyi (HGR) maximal correlation coefficient.
result Significant improvements in bias mitigation compared to existing methods.
Study online learning in RKHS with dependent processes, focusing on \(β\)- and \(φ\)-mixing.
problem Online learning in RKHS with dependent data.
method Online regularized learning algorithm in RKHS, analyzing \(β\)- and \(φ\)-mixing sequences.
result Probabilistic upper bounds and convergence rates for mixing coefficients.
Bayesian approach improves network lasso for multi-task learning.
problem Improving the determination of relational coefficients in network lasso.
method Proposes a Bayesian approach to solve multi-task learning problems using network lasso.
result Objective determination of relational coefficients through Bayesian estimation.
We consider the dictionary learning problem, where the aim is to model the given data as a linear combination of a few columns of a matrix known as a dictionary, where the sparse weights forming the linear combination are known as coefficients. Since the dictionary and coefficients, parameterizing the linear model are …
We consider the problem of recovering block-sparse signals whose structures are unknown \emph{a priori}. Block-sparse signals with nonzero coefficients occurring in clusters arise naturally in many practical scenarios. However, the knowledge of the block structure is usually unavailable in practice. In this paper, we d…
Improves functional linear regression with shape transfer learning.
problem Data scarcity in functional linear models.
method Shape-based transfer learning from auxiliary to target domains.
result Enhances robustness and generalizability of functional linear models.
We consider the problem of sparse coding, where each sample consists of a sparse linear combination of a set of dictionary atoms, and the task is to learn both the dictionary elements and the mixing coefficients. Alternating minimization is a popular heuristic for sparse coding, where the dictionary and the coefficient…
We study learning problems in which the conditional distribution of the output given the input varies as a function of additional task variables. In varying-coefficient models with Gaussian process priors, a Gaussian process generates the functional relationship between the task variables and the parameters of this con…
New method improves DAG learning by using large coefficients for higher-order terms.
problem Recovering DAG structures from observational data is challenging due to combinatorial optimization.
method Proposes truncated matrix power iteration to approximate DAG constraints efficiently.
result Empirically outperforms previous methods by a factor of 3 or more in structural Hamming distance.
The paper debiases machine learning predictions to correct bias in regression coefficients.
problem Bias in regression coefficients from machine learning predictions.
method Proposes an adversarial machine learning algorithm to de-bias predictions.
result Adversarial predictions recover true coefficients, while naive predictions are biased.
AER dynamically adjusts entropy regularization for better LLM reinforcement learning.
problem Policy entropy collapse in RLVR training limits exploration and reasoning performance.
method Adaptive Entropy Regularization (AER) with difficulty-aware coefficient allocation, initial-anchored target entropy, and dynamic global coefficient adjustment.
result AER consistently outperforms baselines on mathematical reasoning benchmarks, improving both accuracy and exploration.
MLShrink integrates machine learning with wavelet shrinkage for denoising.
problem Denoising signals with uncertain magnitudes
method Combines wavelet shrinkage with machine learning
result Preserves simplicity for signal coefficients while allowing data-adaptive decisions for ambiguous coefficients
This paper addresses parameter estimation for wave equations with Markovian switching.
problem Parameter estimation for wave equations with abrupt changes.
method Bayesian statistical framework using discrete sparse Bayesian learning.
result Strong performance in parameter estimation for variable coefficient PDEs.
Filter banks are a popular tool for the analysis of piecewise smooth signals such as natural images. Motivated by the empirically observed properties of scale and detail coefficients of images in the wavelet domain, we propose a hierarchical deep generative model of piecewise smooth signals that is a recursion across s…
Improved model-free reinforcement learning with decision-estimation coefficient.
problem Interactive decision making, including structured bandits and reinforcement learning.
method Combining Estimation-to-Decisions with optimistic estimation to achieve better regret bounds.
result Regret bounds for model-free reinforcement learning with value function approximation.
Motivated by value function estimation in reinforcement learning, we study statistical linear inverse problems, i.e., problems where the coefficients of a linear system to be solved are observed in noise. We consider penalized estimators, where performance is evaluated using a matrix-weighted two-norm of the defect of …
The Statistical Learning Theory (SLT) provides the theoretical guarantees for supervised machine learning based on the Empirical Risk Minimization Principle (ERMP). Such principle defines an upper bound to ensure the uniform convergence of the empirical risk Remp(f), i.e., the error measured on a given data sample, to …
Global information is essential for dense prediction problems, whose goal is to compute a discrete or continuous label for each pixel in the images. Traditional convolutional layers in neural networks, initially designed for image classification, are restrictive in these problems since the filter size limits their rece…
We consider a nonlinear state-space model with the state transition and observation functions expressed as basis function expansions. The coefficients in the basis function expansions are learned from data. Using a connection to Gaussian processes we also develop priors on the coefficients, for tuning the model flexibi…
NGD models have higher effective dimension than SGD models.
problem Measuring model complexity accurately.
method Comparison of NGD and SGD models using effective dimension measures.
result NGD models have a higher effective dimension than SGD models.
New loss function improves accuracy of MRI parameter estimation.
problem Systematic errors in parameter estimates at low SNR.
method Developed and implemented negative log Rician likelihood (NLR) loss.
result NLR loss shows higher accuracy in parameter estimation than MSE loss at low SNR.
Bayesian method discovers PDEs with variable coefficients robustly.
problem Discovering PDEs from noisy data is challenging.
method Bayesian sparse learning with tBGL-SS and Gibbs sampler.
result Method enhances robustness and model selection criteria.
New bounds show complexity of adversarial decision making.
problem Understanding sample efficiency in adversarial decision making.
method New upper and lower bounds on Decision-Estimation Coefficient.
result Decision-Estimation Coefficient is necessary and sufficient for low regret in adversarial decision making.
Adaptive transfer learning model for varying mechanisms across domains.
problem Improving inference in a target domain by leveraging related source domains with varying mechanisms.
method Semi-parametric domain-varying coefficient model (DVCM) for structured transfer learning.
result Minimax rate-optimal adaptive transfer learning estimator with provable negative transfer safeguards.
New method for MTL with varying sparsity patterns across tasks.
problem Jointly training multiple linear models with differing sparsity patterns.
method Mixed-integer programming formulation and scalable algorithms.
result Our methods leverage shared support information to improve variable selection.
Examines learning efficiency in neural networks and related models.
problem Analyzing efficiency in deep learning models with singular learning coefficients.
method Examined learning coefficients in neural networks and three-layer neural networks with ReLU units.
result Extended results to include Softmax function, providing a broader understanding of learning efficiency.
Study shows LLC correlates with neural network compressibility.
problem Evaluating limits of neural network compression.
method Extended minimum description length principle using singular learning theory.
result Complexity estimates based on LLC are linearly correlated with compressibility.
This work addresses unstable MeanFlow training by optimizing a coefficient in the loss function.
problem Unstable training of MeanFlow models with non-decreasing loss and unbounded gradient variance.
method Established a theory attributing the instability to misuse of the conditional velocity field, derived the optimal coefficient, and showed practical realizations.
result Optimal coefficient yields up to 54% improvement in sample quality and monotone FID trend.
In this short report, we investigate the ability of the DCCA coefficient to measure correlation level between non-stationary series. Based on a wide Monte Carlo simulation study, we show that the DCCA coefficient can estimate the correlation coefficient accurately regardless the strength of non-stationarity (measured b…
Machine learning improves aircraft performance prediction by analyzing flight data.
problem Limited aircraft performance models based on industry-wide guidelines.
method Use machine learning on flight data to estimate drag and lift coefficients.
result Excellent accuracy in real-life data, supporting aerodynamics principles.
Introduces LLC, a new complexity measure for DNNs based on SLT.
problem Lack of effective complexity measures for DNNs.
method Uses Singular Learning Theory to define LLC and proposes scalable estimator.
result Empirical evidence shows LLC provides valuable insights into DNN complexity.
Formula connects linking coefficients to Kontsevich integral coefficients.
problem Linking coefficients from Kontsevich integral.
method Purely combinatorial approach.
result Expresses linking coefficients as combinations of Kontsevich integral coefficients.
Proposes a model for time-varying regression coefficients.
problem Uncertainty in forecasting due to changing correlations over time.
method Adopting state space literature, models how regression coefficients change over time.
result Accurate estimates for continuous outcomes but fails for binary outcomes.
We present a machine learning algorithm for the prediction of molecule properties inspired by ideas from density functional theory. Using Gaussian-type orbital functions, we create surrogate electronic densities of the molecule from which we compute invariant "solid harmonic scattering coefficients" that account for di…
Generalizes underlap coefficient for multivariate group separation.
problem Quantifying distributional separation across groups in statistical learning.
method Generalizes underlap coefficient (UNL) to multivariate settings, studies its relationship with Bayes risk and mutual information, proposes an efficient importance sampling estimator.
result UNL as a measure of dependence between group labels and variables of interest, interpretable measure of partition-covariate dependence in clustering.
Activity coefficients, which are a measure of the non-ideality of liquid mixtures, are a key property in chemical engineering with relevance to modeling chemical and phase equilibria as well as transport processes. Although experimental data on thousands of binary mixtures are available, prediction methods are needed t…
The paper introduces a machine learning method to forecast market direction using efficient frontier coefficients.
problem Improving asset return estimation for portfolio optimization.
method Monthly directional market forecast using an online decision tree trained on efficient frontier coefficients.
result The method outperforms baseline portfolios and other feature sets.
In statistical classification and machine learning, as well as in social and other sciences, a number of measures of association have been proposed for assessing and comparing individual classifiers, raters, as well as their groups. In this paper, we introduce, justify, and explore several new measures of association, …
Algorithm estimates bounds of updated classifier coefficients efficiently.
problem Determining sensitivity of updated classifiers without retraining.
method Proposes an algorithm to estimate upper and lower bounds of updated classifier coefficients.
result Estimates bounds with low computational complexity and tightness.
This paper presents an infinite variational autoencoder (VAE) whose capacity adapts to suit the input data. This is achieved using a mixture model where the mixing coefficients are modeled by a Dirichlet process, allowing us to integrate over the coefficients when performing inference. Critically, this then allows us t…
Computed distortion coefficients for the α-Grushin plane.
problem Analyzing the distortion coefficients of the α-Grushin plane.
method Using generalised trigonometric functions and synthetic curvature conditions.
result Estimates for distortion coefficients and a curvature condition conjecture.
Improved SVRG with a coefficient reduces training loss in deep learning.
problem Demonstrating SVRG's effectiveness in deep learning.
method Introduced a multiplicative coefficient α to control SVRG's variance reduction strength and decay it linearly.
result α-SVRG consistently reduces training loss compared to baseline and standard SVRG across various model architectures and datasets.