This note improves code quality for equientropic channels by maximizing marginal entropy.
problem Improving code quality for equientropic channels with finite bit usage.
method Characterizes code quality by an upper bound on expected minimum error probability for equientropic channels, showing random coding maximizes marginal entropy.
result For equientropic channels, random coding maximizes marginal entropy and achieves minimal upper bound on expected minimum error probability.
Optimal policy for multi-hypothesis testing with controlled sensing to minimize delay and error.
problem Minimizing delay in multi-hypothesis testing with controlled sensing.
method Designing a policy to control the delay while ensuring error probability constraint.
result Policy achieves information-theoretic lower bound on expected delay asymptotically.
Paper generalizes EC inference for loopy models.
problem Probabilistic inference in loopy models.
method Generalized Expectation Consistency (GEC) method.
result GEC can be applied to MAP and MMSE estimation.
Proposes a robust risk measure to minimize capital errors.
problem Minimizing capital determination errors due to risk overestimation and underestimation.
method Uses supremum over probability measures to minimize overestimation and underestimation costs.
result Guarantees the existence of a solution and explores properties of minimizer and minimum as risk and deviation measures.
Algorithm reduces historical expected shortfall computation by focusing on worst-case scenarios.
problem Computing the historical expected shortfall efficiently and accurately.
method Multi-step algorithm using Monte Carlo simulations to identify and reduce the number of worst-case scenarios.
result Non-asymptotic bounds for the L p-error of the expected shortfall estimator are derived.
MPF method improves parameter estimation in probabilistic models.
problem Difficulty in fitting probabilistic models due to intractable partition function.
method Minimum Probability Flow (MPF) method for parameter estimation.
result MPF outperforms existing techniques in convergence time and accuracy.
Paper proposes deep neural networks for nonparametric regression from dependent data.
problem Nonparametric regression from strongly mixing observations.
method Minimum error entropy principle applied to deep neural networks.
result Deep neural networks achieve minimax optimal convergence rates for Gaussian errors.
New training method for ASR models reduces word error rate.
problem Traditional ASR training methods do not directly optimize word error rate.
method Training attention-based models to minimize expected word error rate using N-best lists.
result Improved performance by up to 8.2% compared to baseline.
Review of diversification models finds simple rules still best.
problem Testing new diversification models for out-of-sample performance.
method Tested sixteen strategies across six datasets.
result No new models consistently outperform simple diversification rules.
Introduces RMEE for robust classification, improving MEE's performance in noisy conditions.
problem Improving robustness of MEE criterion for noisy classification.
method Analyzed optimal error distribution, introduced RMEE with half-quadratic optimization.
result RMEE achieves better robustness in noisy conditions compared to original MEE.
Bayesian method recovers causal structure in SEMs with equal error variances.
problem Recovering causal structure in SEMs with equal error variances.
method Bayesian DAG selection method using g-priors and the key property of minimum expected squared errors.
result The method consistently recovers the true graph without additional distributional assumptions.
CTS improves combinatorial optimization in unknown environments.
problem Optimizing actions from a large set of alternatives in unknown environments.
method Combinatorial Thompson Sampling (CTS) for semi-bandit feedback.
result CTS achieves optimal regret bounds in various networking problems.
Defines MER for Bayesian learning, a gap between achievable and optimal performance.
problem Analyzing the best performance of Bayesian learning under generative models.
method Two methods for deriving upper bounds for MER: conditional mutual information and minimum estimation error.
result Quantifies the rate at which MER decays to zero with more data and relates it to model richness.
Inflating the minimum norm interpolator improves linear regression generalization error.
problem Highly anisotropic covariances and diverging d/n in linear regression. method Inflating the minimum ℓ2 norm interpolator by a constant greater than one. result Inflating the minimum norm interpolator improves generalization error.
Motivated by problems of anomaly detection, this paper implements the Neyman-Pearson paradigm to deal with asymmetric errors in binary classification with a convex loss. Given a finite collection of classifiers, we combine them and obtain a new classifier that satisfies simultaneously the two following properties with …
Proposes a method to solve deep neural networks' local minimum problem.
problem Local minimum problem in deep neural networks training.
method Transforms cross-entropy loss into risk-averse error criterion, adjusts RSI, and uses convexity region.
result Trained deep learning machine is expected to be inside a global minimum's attraction basin.
Near-optimal tests and confidence sequences for non-parametric data.
problem Flexible statistical inference and decision-making with non-parametric data.
method Classic delayed-start normal-mixture sequential probability ratio tests with asymptotic guarantees.
result Asymptotically optimal type-I error and expected rejection time guarantees.
This paper optimizes speech recognition WER via sampling.
problem Improving word error rate (WER) in speech recognition.
method Optimizing expected WER by sampling paths from lattices used in sMBR training.
result Optimizing WER during acoustic model training gives a 5% relative improvement in WER.
CTS reduces regret in probabilistically triggered combinatorial bandits.
problem Optimizing decisions with probabilistically triggered arms in combinatorial multi-armed bandits.
method Combinatorial Thompson Sampling (CTS) with a regret bound analysis.
result Derives an O(∑i=1mlogT/(piΔi)) regret bound for CTS. A new KM clustering algorithm reduces error and scales to large datasets.
problem Traditional KM error analyses suffer from generalization gaps and lack true error bounds.
method Formalized true K-Medoids error, decomposed into ME and MME, provided convergence result, proposed MCPAM algorithm.
result MCPAM achieves true error bounds and scales to 1 billion points.
Improved community detection in heterogeneous SBM with side information.
problem Misclassification in community detection with noisy labels.
method Optimal weighted message passing and minimum energy flow.
result Optimal weighting improves misclassification rate in heterogeneous SBM.
We study high-dimensional asymptotic performance limits of binary supervised classification problems where the class conditional densities are Gaussian with unknown means and covariances and the number of signal dimensions scales faster than the number of labeled training samples. We show that the Bayes error, namely t…
We refine Expected Shortfall by controlling different tail portions, offering tailored risk assessments.
problem Risk assessment in financial positions, especially in tail regions.
method Introducing adjusted Expected Shortfall measures that control different tail portions.
result Adjusted Expected Shortfall measures ensure risk does not exceed specified thresholds for various probability levels.
Probability calibration trees improve accuracy of probability estimates.
problem Improving accuracy and calibration of probability estimates from classifiers.
method Probability calibration trees modify logistic model trees to learn different models in regions of the input space.
result Probability calibration trees outperform isotonic regression and Platt scaling in terms of root mean squared error.
Let X be a data matrix of rank ρ, whose rows represent n points in d-dimensional space. The linear support vector machine constructs a hyperplane separator that maximizes the 1-norm soft margin. We develop a new oblivious dimension reduction technique which is precomputed and can be applied to any input matrix X. We pr…
Study minimax off-policy evaluation in multi-armed bandits with known and unknown behavior policies.
problem Evaluate policies in multi-armed bandits with unknown behavior policies.
method Develop minimax rate-optimal procedures for known and unknown behavior policies, including the Switch estimator and Chebyshev polynomial-based estimator.
result Plug-in estimator achieves optimal competitive ratio up to a logarithmic factor when behavior policy is unknown.
This paper argues against using calibration metrics for assessing posterior probabilities and proposes expected proper scoring rules instead.
problem The assessment of posterior probabilities generated by machine learning classifiers using calibration metrics is flawed and should be replaced with expected proper scoring rules.
method The paper reviews proper scoring rules from a practical perspective, explains why expected PSRs are a principled measure of posterior quality, and introduces a new calibration metric called calibration loss.
result Calibration loss is superior to expected calibration error and expected score divergence calibration metrics for assessing posterior probabilities.
Inference for normal and Monte Carlo distributions using minimum relative entropy.
problem Inference from partial information on expectations and covariances.
method Minimum relative entropy sub-manifolds, analytical formulas, Monte Carlo simulations.
result Improved numerical implementation for inference from partial information.
New bounds on machine learning model generalization error moments.
problem Understanding the performance of machine learning models.
method Information-theoretic bounds on the moments of the generalization error of learning algorithms.
result Proposed bounds on generalization error moments and their high-probability bounds.
We compute the expected value of the Kullback-Leibler divergence to various fundamental statistical models with respect to canonical priors on the probability simplex. We obtain closed formulas for the expected model approximation errors, depending on the dimension of the models and the cardinalities of their sample sp…
The paper describes fitting submanifolds to data using Sussmann's orbit theorem.
problem Fitting an immersed submanifold to random samples.
method Uses Sussmann's orbit theorem to ensure submanifold fitting. Reconstruction involves encoding times and decoding via flows of vector fields.
result A high-probability bound on excess risk for the reconstruction error.
Estimates the dimension of Kronecker product models using Jacobian rank and tropical morphism.
problem Estimating the dimension of Kronecker product models.
method Using Jacobian rank and tropical morphism to describe the limit of the model.
result Combinatorial conditions for the expected dimension and proof for binary restricted Boltzmann machine.
The study tightens bounds on binomial probabilities and minimums using KL-divergence.
problem Tightening bounds on binomial probabilities and minimums of i.i.d. Binomials.
method Applied Sanov's theorem to derive upper and lower bounds on binomial tail probabilities and minimums, expressed in terms of KL-divergence.
result High probability upper and lower bounds on the minimum of i.i.d. Binomial random variables, finite sample, asymptotically tight.
Study finds the minimum number of finite Gaussian mixtures for best approximation.
problem Finding the minimum number of finite Gaussian mixtures for best approximation.
method Local moment matching for upper bound and spectral analysis for lower bound.
result Corrects a previous lower bound in the case of Gaussian mixing distributions.
This paper shows faster convergence rates for stochastic gradient descent in binary classification.
problem Achieving faster convergence rates for stochastic gradient descent in binary classification.
method Stochastic gradient descent and averaging variant, focusing on exponential convergence rates under strong low-noise conditions.
result Exponential convergence of the expected classification error in the final phase of stochastic gradient descent and averaged stochastic gradient descent for differentiable convex loss functions.
New truthful calibration errors improve model ranking in multiclass prediction.
problem Non-truthful calibration errors can mislead model comparisons.
method Introduced perfectly truthful calibration errors for multiclass predictions.
result Truthful calibration errors preserve decision-theoretic dominance and stabilize model rankings.
Exact expressions for double descent and implicit regularization in over-parameterized models.
problem Understanding the generalization error of over-parameterized models like deep neural networks.
method Surrogate random design to replace standard i.i.d. design, leading to exact expressions for mean squared error and implicit regularization.
result Exact non-asymptotic expressions for double descent and implicit regularization in over-parameterized models.
Study contextual bandits with stage-wise constraints, proving regret bounds and extending results.
problem Contextual bandits with stage-wise constraints in high probability and expectation settings.
method Upper-confidence bound algorithms for linear and non-linear reward/cost functions, extending to multiple constraints.
result Regret bounds for various settings, including non-linear reward/cost functions.
Proposes a new parametric thresholding algorithm for NP classification without requiring minimum sample size on class 0.
problem Achieving minimal type II error while controlling type I error in binary classification, especially in rare disease diagnosis.
method Employed parametric linear discriminant analysis (LDA) and proposed a new thresholding algorithm.
result Proves NP oracle inequalities for one classifier, benefiting from explicit parametric model assumption.
Sample size determination for a data set is an important statistical process for analyzing the data to an optimum level of accuracy and using minimum computational work. The applications of this process are credible in every domain which deals with large data sets and high computational work. This study uses Bayesian a…
New decision-theoretic calibration error metric improves prediction reliability.
problem Improving the reliability of predictions for decision-making.
method Proposed Calibration Decision Loss (CDL) and an efficient algorithm to achieve near-optimal CDL.
result Near-optimal CDL guarantees vanishing payoff loss from miscalibration.
The MoN loss fails to accurately represent ground truth probability density functions in probabilistic trajectory prediction.
problem Improving the diversity of probabilistic trajectory predictions in autonomous driving and robot planning.
method Proof and validation of the MoN loss's inaccuracy and proposed solutions to correct it.
result The MoN loss approximates the square root of the ground truth probability density function, not the function itself.
The study analyzes robustness of estimators in linear models with adversarial errors.
problem Analyzing robustness of estimators in linear models with adversarial errors.
method Develops a general theory for minimum norm interpolating estimators and RERM in linear models without conditions on errors.
result Quantitative bound for the prediction error relating it to Rademacher complexity, norm of minimum norm interpolator of errors, and subdifferential size.
The paper clusters sequences from unknown distributions using k-medoids.
problem Clustering sequences from unknown composite distributions.
method k-medoids algorithm for sequences with composite distributions.
result Error probability decreases exponentially with increasing sample size.
A new calibration metric bridges testability and actionability.
problem Combining testability and actionable insights for forecast probabilities.
method Cutoff Calibration Error (CCE) that assesses calibration over intervals of forecasted probabilities.
result Cutoff Calibration Error is both testable and actionable.
Optimal estimator derived for partially observable LTI systems.
problem Optimal estimator for partially observable LTI systems.
method State-space representation for derivation of optimal estimator.
result Derivation of minimum error variance estimator for partially observable LTI systems.
In his seminal work, Schapire (1990) proved that weak classifiers could be improved to achieve arbitrarily high accuracy, but he never implied that a simple majority-vote mechanism could always do the trick. By comparing the asymptotic misclassification error of the majority-vote classifier with the average individual …
Paper finds how many neurons are needed to approximate histogram distributions.
problem How many neurons are needed to approximate a target probability distribution?
method Examined for uniform input distribution and histogram target distributions, using efficient neural net construction.
result Obtained a new upper bound on the number of required neurons, strictly better than previous bounds.