We consider the problem of learning a dictionary matrix from a number of observed signals, which are assumed to be generated via a linear model with a common underlying dictionary. In particular, we derive lower bounds on the minimum achievable worst case mean squared error (MSE), regardless of computational complexity…
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48 results for “minimax MSE”
A recently proposed SLOPE estimator (arXiv:1407.3824) has been shown to adaptively achieve the minimax estimation rate under high-dimensional sparse linear regression models (arXiv:1503.08393). Such minimax optimality holds in the regime where the sparsity level , sample size , and dimension satisfy …
The paper analyzes convergence rates of Gaussian process approximations for scalable regression.
problem Characterizing convergence rates of Gaussian process approximations for scalable regression.
method Analysis of kernel functions and dataset-size for isotropic kernels like Matérn and squared-exponential.
result Upper and lower bounds on predictive MSE and calibration metric convergence rates are derived.
We study the off-policy evaluation problem---estimating the value of a target policy using data collected by another policy---under the contextual bandit model. We consider the general (agnostic) setting without access to a consistent model of rewards and establish a minimax lower bound on the mean squared error (MSE).…
Multi-task Linear Regression without Eigenvalue Lower Bounds: Adaptivity, Robustness, and Safetystat.ML
New estimator tackles multi-task linear regression with outliers, avoiding eigenvalue lower bounds.
problem Multi-task linear regression with contaminated tasks and eigenvalue lower bounds failure.
method Matrix-weighted norm regularization and relative balancedness condition.
result Prediction MSE bounds match Duan and Wang (2023) under weaker spectral assumptions.
We consider the problem of dictionary learning under the assumption that the observed signals can be represented as sparse linear combinations of the columns of a single large dictionary matrix. In particular, we analyze the minimax risk of the dictionary learning problem which governs the mean squared error (MSE) perf…
Study shows MSE with sigmoid can match SCE in classification tasks, especially with noisy data.
problem Inconsistent errors in neural network classification tasks.
method Introduced Output Reset algorithm to use MSE with sigmoid activation.
result MSE with sigmoid activation achieves comparable accuracy and convergence rates to Softmax Cross-Entropy, especially in noisy data scenarios.
Deep nets trained with MSE loss exhibit Neural Collapse, collapsing features and classifiers to class means.
problem Understanding Neural Collapse in MSE-trained deep nets.
method Developed a new MSE loss decomposition and introduced the central path concept.
result Exact dynamics of Neural Collapse along the central path can be predicted.
This article presents valuation of Treasury Bonds (T-Bonds) on Macedonian Stock Exchange (MSE) and empirical test of duration, modified duration and convexity of the T-bonds at MSE in order to determine sensitivity of bonds prices on interest rate changes. The main goal of this study is to determine how standard valuat…
Adaptive NN method improves matrix completion for non-smooth data.
problem Matrix completion with non-smooth non-linear functions under high missingness.
method Two-sided nearest neighbors with \Holder function class non-linearity.
result NN error rate matches oracle's for latent factors, non-trivial for wide range of missingness.
The Many-to-Many Mapping Between the Concordance Correlation Coefficient and the Mean Square Errorcs.LG
We derive the mapping between two of the most pervasive utility functions, the mean square error () and the concordance correlation coefficient (CCC, ). Despite its drawbacks, is one of the most popular performance metrics (and a loss function); along with lately in many of the sequence prediction…
Gaussian surrogates improve Poisson imaging performance at low doses.
problem Improving Poisson imaging performance at low doses.
method Analysis of Poisson and Gaussian surrogate reconstruction objectives under Poisson noise.
result Gaussian surrogates can achieve MSE comparable to Poisson MAP at low doses.
The Theory and Practice of Highly Scalable Gaussian Process Regression with Nearest Neighboursstat.ML
Develops a theoretical framework for scalable Gaussian Process regression methods.
problem Limited scalability of Gaussian Process regression for large datasets.
method Introduces and analyzes Nearest Neighbour Gaussian Process (NNGP) and scalable GPnn methods.
result Derives almost sure pointwise limits for predictive criteria and proves risk minimax rates.
New model estimates signals from noisy data using robust optimization.
problem Estimating signals from noisy observations with uncertainty.
method Wasserstein distributionally robust optimization for minimax MSE estimation.
result Nash equilibrium found for optimal estimator and prior.
This work justifies neural collapse under MSE loss and analyzes the optimization landscape.
problem Understanding neural collapse in deep neural networks under MSE loss.
method Global landscape analysis of vanilla nonconvex MSE loss.
result The only global minimizers are neural collapse solutions.
In this manuscript we propose two objective terms for neural image compression: a compression objective and a cycle loss. These terms are applied on the encoder output of an autoencoder and are used in combination with reconstruction losses. The compression objective encourages sparsity and low entropy in the activatio…
New estimators outperform maximum likelihood without hyper-parameter estimation.
problem Improving system identification performance without hyper-parameter estimation.
method Developed generalized Bayes and closed-form biased estimators using excess MSE.
result New estimators have comparable performance to empirical-Bayes-based regularized estimator.
Deep learning detects microsleep episodes in EEG data.
problem Automatic detection of microsleep episodes (MSEs) in EEG data.
method Convolutional neural networks (CNNs) and LSTM networks were implemented to analyze MWT data.
result Deep learning algorithms showed good performance close to human experts in detecting MSEs.
Heterogeneous Information Network based Default Analysis on Banking Micro and Small Enterprise Usersq-fin.RM
Paper proposes HIDAM model to improve MSE default risk assessment using heterogeneous information networks.
problem Default risk assessment for MSEs due to lack of credit information and diverse financial activities.
method HIDAM model incorporating heterogeneous information networks with multi-typed nodes and links, extracting interactive information through meta-paths, and using a hierarchical attention mechanism.
result HIDAM model outperforms state-of-the-art competitors on real-world banking data.
Noise in imputed values corrects biases in machine learning models.
problem Systematic biases in imputed values affect downstream analyses.
method Introducing noise to imputed values to correct biases.
result Noise-corrected imputation methods produce unbiased estimates.
Sampling and Reconstruction of Graph Signals via Weak Submodularity and Semidefinite Relaxationstat.ML
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…
This paper solves hedging in incomplete markets using neural networks.
problem Hedging in incomplete markets with risk factor, illiquidity, and discrete transaction dates.
method Proposes a jump-diffusion model and uses RNN, LSTM, and Mogrifier-LSTM neural networks for hedging strategies.
result Mogrifier-LSTM is the fastest and most effective model for hedging.
CAEL-MIPS learns embeddings to improve MIPS for better OPE in contextual bandits.
problem High variance in IPS weighting for OPE in large action spaces.
method Context-Action Embedding Learning (CAEL) for MIPS to minimize MSE.
result CAEL-MIPS outperforms baselines in MSE for OPE in contextual bandits.
The paper explains why estimating a history-dependent policy can reduce MSE in reinforcement learning.
problem Understanding why history-dependent policies can improve MSE in off-policy evaluation.
method The paper derives a bias-variance decomposition of MSE for various OPE estimators, showing how history-dependent policies can decrease variance and increase bias.
result History-dependent policies can decrease the variance of importance sampling estimators, leading to lower MSE.
A new KF handles outliers without MSE loss.
problem Outliers degrade Kalman filter performance.
method NUV priors, EM and AM for variance estimation.
result Outlier-insensitive KF outperforms existing methods.
Replacing MSE with f-divergence in diffusion models improves robustness under data contamination.
problem Improving robustness of diffusion models under data contamination.
method Replacing MSE with f-divergence in diffusion models.
result Empirical improvement in performance under data contamination.
The paper explores MAE as a loss function for DNN vector-to-vector regression, proving its advantages over MSE.
problem Improving loss function for deep neural network based vector-to-vector regression.
method Presenting performance bounds and new properties of MAE, deriving generalized upper bounds, and interpreting MAE as a Laplacian distribution.
result MAE is a more suitable loss function than MSE for DNN based vector-to-vector regression, especially when errors follow a Laplacian distribution.
Study on LMMSE estimation with model mismatch, quantifying MSE trade-offs.
problem Model mismatch in LMMSE estimation with undermodeling.
method Analyzing the average MSE of LMMSE estimation with random regressors.
result Performance improvement depends on sufficient samples and model complexity.
A new complexity measure MDL-COMP for overparameterized models improves generalization performance.
problem Complexity measures based on Rissanen's MDL principle are not well-suited for overparameterized models.
method Developed a novel MDL-based complexity (MDL-COMP) for overparameterized models, defined via an optimality criterion over Ridge estimators.
result MDL-COMP scales linearly with when , but exponentially smaller for ; it upper bounds in-sample MSE.
In this paper, we derive Hybrid, Bayesian and Marginalized Cramér-Rao lower bounds (HCRB, BCRB and MCRB) for the single and multiple measurement vector Sparse Bayesian Learning (SBL) problem of estimating compressible vectors and their prior distribution parameters. We assume the unknown vector to be drawn from a compr…
Improved covariance matrix estimation for multiple classes with limited data.
problem Estimating covariance matrices for multiple classes with scarce data.
method Coupled regularized sample covariance matrix estimator (RSCM) that combines pooled SCM and scaled identity matrix for regularization.
result The coupled RSCM estimators outperform cross-validation in classification tasks with comparable accuracy but faster computation.
Paper proposes a new autoencoder metric for balanced learning in imbalanced tabular datasets.
problem Challenges of imbalanced self-supervised learning in tabular data.
method Developed a Multi-Supervised Balanced MSE metric to balance learning.
result The new metric outperforms standard MSE in imbalanced datasets.
Enhances ENet's prediction accuracy while maintaining uncertainty estimation.
problem Gradient shrinkage problem in ENet's loss function.
method Proposes a multi-task learning framework with a modified MSE loss function.
result Improves ENet's prediction accuracy without losing uncertainty estimation.
Bagging can significantly improve the generalization performance of unstable machine learning algorithms such as trees or neural networks. Though bagging is now widely used in practice and many empirical studies have explored its behavior, we still know little about the theoretical properties of bagged predictions. In …
Optimized AIS scheme reduces bias and MSE for general proposals.
problem Performing Monte Carlo integration with general proposals.
method Global optimization of χ²-divergence using stochastic gradient Langevin dynamics.
result Explicit theoretical guarantees for uniform-in-time MSE reduction.
New statistical methods improve explainability of boosting models.
problem Uncertainty quantification for boosting models is computationally intensive and hard to interpret.
method Derive methods for statistical inference using gradient boosting and Boulevard regularization.
result Achieve asymptotically normal predictions with theoretical guarantees and runtime independent of data size.
Modern CATE models often fail to outperform a trivial zero-effect predictor, highlighting significant challenges.
problem Lack of robustness in CATE models when applied to real-world data.
method Large-scale benchmark study using diverse observational sampling strategies and novel statistics.
result 62% of CATE estimates have higher MSE than a trivial zero-effect predictor, indicating poor performance.
The paper analyzes a simple neural network model with algebraic methods.
problem Finding minima of a ridge-regularized mean squared error for ReLU perceptrons.
method Developed a Divide-Enumerate-Merge strategy using computational algebra.
result Identifies both isolated and connected minima of the RR-MSE.
While the objective in traditional multi-armed bandit problems is to find the arm with the highest mean, in many settings, finding an arm that best captures information about other arms is of interest. This objective, however, requires learning the underlying correlation structure and not just the means of the arms. Se…
BASIS: Batchwise Advantage Estimation from Single-Rollout Information Sharing for LLM Reasoningcs.LG
BASIS improves LLM reasoning by sharing batchwise rollout info, reducing MSE by 69%.
problem Improving large language model reasoning with limited rollouts and batch information.
method BASIS samples only one rollout per prompt but uses batch information to improve value function estimation.
result BASIS reduces MSE in value function estimation by 69% compared to REINFORCE++.
New analysis reveals optimal regularization for ESNs, avoiding double descent.
problem Characterizing and optimizing Echo State Networks (ESNs) for precise bias-variance.
method Random matrix theory applied to ESNs in a teacher-student setting.
result ESNs achieve lower MSE with limited training samples and teacher memory.
Paper introduces a new cost function to improve deep learning model generalization.
problem Overfitting and poor extrapolation of deep learning models.
method Introduces a 'whitening' cost function based on the Ljung-Box statistic.
result Significant improvement in generalization for RNNs and image autoencoders.
Proposes an efficient shrinkage path for ridge regression.
problem Ill-conditioned data in linear models.
method A new generalized ridge regression shrinkage path that minimizes MSE risk.
result The path is as short as possible while maintaining optimal trade-off.
With the recent advancement in the deep learning technologies such as CNNs and GANs, there is significant improvement in the quality of the images reconstructed by deep learning based super-resolution (SR) techniques. In this work, we propose a robust loss function based on the preservation of edges obtained by the Can…
Most of existing manifold learning methods rely on Mean Squared Error (MSE) or norm. However, for the problem of image quality assessment, these are not promising measure. In this paper, we introduce the concept of an image structure manifold which captures image structure features and discriminates image dist…
Bias-Variance Tradeoff in a Sliding Window Implementation of the Stochastic Gradient Algorithmstat.ML
The paper analyzes SW-SGD for MSE in biased and variance-reduced gradient estimators.
problem Analyzing MSE of SW-SGD in biased and variance-reduced gradient estimators.
method Using asymptotic normality, the paper characterizes SW-SGD's mean and variance, proving convergence and showing SW-SGD's superiority over SGD.
result SW-SGD incurs lower MSE than SGD on quadratic and convex problems.
In this paper, we continue our previous work on the Dirichlet mixture model (DMM)-based VQ to derive the performance bound of the LSF VQ. The LSF parameters are transformed into the LSF domain and the underlying distribution of the LSF parameters are modelled by a DMM with finite number of mixture components. The…
The study establishes risk bounds for distributional regression estimators.
problem Estimating distributional regression models with nonparametric methods.
method Theoretical bounds for CRPS and MSE are derived for convex and non-convex constraints.
result Theoretical risk bounds are validated through experiments on simulated and real data.