Gradient descent converges to minimum Bayes risk for two-layer ReLU networks in mean field regime.
problem Training two-layer ReLU networks using gradient descent in the mean field regime.
method Describes a condition for convergence to minimum Bayes risk, extending previous results to ReLU-activated networks.
result The condition for convergence does not depend on initialization and concerns weak convergence of network realization.
A statistical decision problem is hidden in the core of option pricing. A simple form for the price C of a European call option is obtained via the minimum Bayes risk, R_B, of a 2-parameter estimation problem, thus justifying calling C Bayes (B-)price. The result provides new insight in option pricing, among others obt…
The problem of estimating a high-dimensional sparse vector θ∈Rn from an observation in i.i.d. Gaussian noise is considered. The performance is measured using squared-error loss. An empirical Bayes shrinkage estimator, derived using a Bernoulli-Gaussian prior, is analyzed and compared with the…
The NL score optimizes speaker recognition tasks.
problem Improving speaker recognition accuracy.
method Established the theory of optimal scores based on normalized likelihood.
result NL score is equivalent to PLDA likelihood ratio under certain conditions.
A new procedure for learning cost-sensitive SVM(CS-SVM) classifiers is proposed. The SVM hinge loss is extended to the cost sensitive setting, and the CS-SVM is derived as the minimizer of the associated risk. The extension of the hinge loss draws on recent connections between risk minimization and probability elicitat…
This paper examines various definitions of adversarial risk and their implications.
problem Quantifying the performance of classifiers under adversarial perturbations.
method Optimal transport, robust statistics, functional analysis, and game theory.
result Generalization of Strassen's theorem and new connections to Choquet capacities and game theory.
We provide a formulation for Local Support Vector Machines (LSVMs) that generalizes previous formulations, and brings out the explicit connections to local polynomial learning used in nonparametric estimation literature. We investigate the simplest type of LSVMs called Local Linear Support Vector Machines (LLSVMs). For…
The study compares clustering risk in Hidden Markov and i.i.d. models, showing the Bayes classifier is nearly optimal.
problem Comparing clustering risk in Hidden Markov and i.i.d. models.
method Analysis of Bayes risk, theoretical bounds, and simulations.
result The Bayes classifier is nearly optimal for clustering in both Hidden Markov and i.i.d. models.
Estimates population profile from small random samples.
problem Learning population composition from limited data.
method Minimum distance estimator based on linear programming.
result Consistent estimation of profile in sublinear sample size.
Study calculates Bayes risk for semi-supervised learning with uncertain labels.
problem Uncertain labeling in semi-supervised classification.
method Gaussian mixture model, Bayes risk computation, comparison with algorithm performance.
result New insights into semi-supervised learning algorithm performance.
New method reduces computational cost for estimating PAC-Bayes bounds.
problem High computational cost in estimating PAC-Bayes bounds.
method General alternative method that makes computational savings.
result Reduces computational cost on the order of the dataset size.
We study the rates of convergence from empirical surrogate risk minimizers to the Bayes optimal classifier. Specifically, we introduce the notion of \emph{consistency intensity} to characterize a surrogate loss function and exploit this notion to obtain the rate of convergence from an empirical surrogate risk minimizer…
The study calculates the risk of semi-supervised multitask learning on Gaussian mixtures.
problem Understanding the risk in semi-supervised multitask learning on Gaussian mixtures.
method Statistical physics methods applied to Gaussian mixture models.
result The study evaluates the performance gain of learning tasks together versus separately.
Lower bounds on Bayes risk for realizable models derived using information theory.
problem Deriving lower bounds on Bayes risk for realizable machine learning models.
method Information-theoretic analysis using rate-distortion theory and mutual information.
result Lower bounds on Bayes risk for realizable models, matching known bounds up to logarithmic factors.
Adversarial consistency depends on the uniqueness of adversarial Bayes classifiers.
problem Consistency of adversarial surrogate losses is not guaranteed.
method Connected consistency of adversarial surrogate losses to the uniqueness of adversarial Bayes classifiers.
result A convex surrogate loss is statistically consistent for adversarial learning if and only if the adversarial Bayes classifier is unique.
The paper develops a new algorithm for constructing minimax estimators using online learning techniques.
problem Designing minimax estimators for probability distribution parameters.
method Viewing the problem as a zero-sum game and using online learning with non-convex losses to find a Nash equilibrium.
result The algorithm constructs both a minimax estimator and a least favorable prior.
PAC-Bayes bound requires prior to place mass on high-performing predictors.
problem Explaining generalization in machine learning.
method Analyzing necessary conditions for PAC-Bayes bounds to provide meaningful generalization guarantees.
result Achieving a target generalisation level requires the prior to place sufficient mass on high-performing predictors.
This research improves binary classification by balancing overfitting and generalization with a novel Bayesian approach.
problem Improving binary classification models to avoid overfitting and generalize well.
method Introduces a PAC-Bayes type learning rule with a balancing parameter λ to balance training error and KL divergence to a prior.
result A choice of λ ensures uniformly vanishing excess loss, even in the agnostic case, by under-regularizing or over-regularizing appropriately.
The digital telecommunications receiver is an important context for inference methodology, the key objective being to minimize the expected loss function in recovering the transmitted information. For that criterion, the optimal decision is the Bayesian minimum-risk estimator. However, the computational load of the Bay…
Meta-learning bounds derived using PAC-Bayes theory for improved generalization.
problem Uncertainty in generalization performance for meta-learning with new tasks.
method PAC-Bayes relative entropy bounds and empirical risk minimization (ERM) method.
result Competitive generalization performance and rapid convergence with data-dependent prior.
New method certifies deep graph classifiers with tighter risk bounds.
problem Certifying the reliability of deep graph classifiers.
method Linearized deep assignment flows with random initial conditions, using PAC-Bayes risk certification.
result Computes tighter out-of-sample risk certificates efficiently.
The paper improves risk certificate tightness for neural networks using PAC-Bayes bounds.
problem Improving the usability of risk certificates for neural networks based on PAC-Bayes bounds.
method Theoretical contributions including KL divergence bounds, efficient methodology for optimization, and methods for optimizing non-differentiable objectives.
result First non-vacuous generalization bounds on CIFAR-10 for neural networks.
This work uses PAC-Bayes for structured prediction with ILE, yielding insights and algorithms.
problem Structured prediction with interdependent outputs and implicit loss embeddings.
method PAC-Bayes perspective applied to ILE framework, deriving generalization bounds and learning algorithms.
result Two learning algorithms derived from PAC-Bayes bounds, analyzed and implemented.
New estimator reduces risk in slate bandits by leveraging Bayes risk criterion.
problem Evaluating slate policies using logged data when policies factorize over slots.
method Developed a new estimator using a control variate approach, showing risk improvement over existing methods.
result The new estimator has lower risk than the pseudoinverse estimator in slate bandit problems.
We present an information-theoretic framework for bounding the number of labeled samples needed to train a classifier in a parametric Bayesian setting. We derive bounds on the average Lp distance between the learned classifier and the true maximum a posteriori classifier, which are well-established surrogates for th…
New PAC-Bayes bounds derived using Legendre transform and f-divergences.
problem Deriving PAC-Bayes bounds under various assumptions.
method Combining Legendre transform and Fenchel--Young inequality to derive change-of-measure inequalities.
result Extended PAC-Bayesian guarantees under tailored assumptions.
Proposes a new risk measurement method for risk-averse stochastic optimization.
problem Risk-averse stochastic optimization problems.
method Develops a risk measure based on argmin and minimum concepts.
result Guarantees the existence of solutions for the proposed problem.
PAC-Bayesian framework for fairness in stochastic and deterministic classifiers.
problem Theoretical guarantees on fairness for balancing predictive risk and fairness constraints.
method PAC-Bayesian framework for both stochastic and deterministic classifiers, covering a broad class of fairness measures.
result Derives generalization bounds for fairness, demonstrating tightness with empirical evaluation.
New method optimises learning via surrogate PAC-Bayes bounds.
problem Computational intractability of optimising generalisation bounds.
method Iteratively optimising surrogate training objectives derived from PAC-Bayes bounds.
result Iteratively optimising surrogates implies optimising original generalisation bounds.
Paper improves risk estimation for extreme events.
problem Estimating extreme risks accurately.
method Modified Bayes risk for expectiles, asymptotic expansions, efficient estimators.
result Asymptotic normality of estimators proved.
PAC-Bayes bounds have been proposed to get risk estimates based on a training sample. In this paper the PAC-Bayes approach is combined with stability of the hypothesis learned by a Hilbert space valued algorithm. The PAC-Bayes setting is used with a Gaussian prior centered at the expected output. Thus a novelty of our …
New PAC-Bayes training method improves model generalization for unbounded loss.
problem Improving generalization of complex models under unbounded loss.
method Established new PAC-Bayes bound for unbounded loss, jointly training prior and posterior.
result Outperforms existing PAC-Bayes training algorithms and matches ERM accuracy.
New data-dependent priors improve PAC-Bayes bounds.
problem Improving PAC-Bayes bounds for nonconvex learning.
method Using data to learn a conditional expectation of the posterior, given a subset of training data.
result Data-dependent oracle priors lead to stronger PAC-Bayes bounds.
In this work, three lattice-free (LF) discriminative training criteria for purely sequence-trained neural network acoustic models are compared on LVCSR tasks, namely maximum mutual information (MMI), boosted maximum mutual information (bMMI) and state-level minimum Bayes risk (sMBR). We demonstrate that, analogous to L…
PAC-Bayes bounds for Gibbs posteriors derived via singular learning theory.
problem Generalization bounds for overparameterized models with data-dependent priors.
method Explicit non-asymptotic PAC-Bayes bounds using singular learning theory.
result Explicit posterior-averaged risk bounds for overparameterized models.
New bound improves on weighted majority vote risk estimation.
problem Improving risk estimation for weighted majority vote.
method Novel Chebyshev-Cantelli inequality and PAC-Bayes-Bennett inequality.
result New bounds improve on existing methods.
Study introduces AMVP and AMRR for dynamic portfolio optimization in volatile markets.
problem Optimizing portfolios in volatile and nonstationary financial markets.
method Adaptive Minimum-Variance Portfolio (AMVP) framework with ARFIMA-FIGARCH processes and non-Gaussian innovations.
result Demonstrated superior performance in risk reduction and portfolio stability during market breaks.
Sequence-to-sequence models, such as attention-based models in automatic speech recognition (ASR), are typically trained to optimize the cross-entropy criterion which corresponds to improving the log-likelihood of the data. However, system performance is usually measured in terms of word error rate (WER), not log-likel…
Paper presents new training methods for neural networks with tighter risk certificates.
problem Training probabilistic neural networks with tighter risk certificates.
method Derived from PAC-Bayes bounds, two training objectives implemented for the first time in neural networks.
result Competitive test set errors and non-vacuous risk bounds with tighter values than previous results.
Batching stabilizes risk in high-dimensional linear regression models.
problem Stability and risk behavior in high-dimensional overparameterized linear regression.
method Minimum-norm overparameterized linear regression model with batch-partitioning.
result Optimal batch size is inversely proportional to noise level and overparametrization ratio, leading to stable risk behavior.
Paper extends transfer learning for decision rules, improving treatment rule estimation.
problem Estimating optimal individualized treatment rules under changing conditions.
method Bayes decision rules and low-dimensional empirical risk minimization.
result Consistent estimators and risk bounds established under mild conditions.
Paper connects two portfolio methods, HRP and Minimum Variance, revealing their underlying similarity.
problem Inability to universally adopt optimization-based portfolio construction methods.
method Unifies Hierarchical Risk Parity and Minimum Variance approaches.
result Schur complementary allocation reveals the connection between HRP and Minimum Variance.
The normalized maximized likelihood (NML) provides the minimax regret solution in universal data compression, gambling, and prediction, and it plays an essential role in the minimum description length (MDL) method of statistical modeling and estimation. Here we show that the normalized maximum likelihood has a Bayes-li…
The paper analyzes risk spillovers between AI ETFs, AI tokens, and green markets.
problem Risk spillovers among AI ETFs, AI tokens, and green markets.
method R2 decomposition method
result AI ETFs and clean energy act as risk transmitters, while AI tokens and green assets act as receivers.
Bayes Error Rate estimators are evaluated for accuracy and sample requirements.
problem Evaluating the accuracy and sample requirements of Bayes Error Rate estimators.
method Monte Carlo simulations with synthetic data and real-world scenarios.
result k-Nearest Neighbor (kNN) is the most accurate non-parametric estimator.
New method certifies risks of LLM outputs, improving accuracy and reliability.
problem Uncertain and incorrect outputs from large language models.
method Information-lift certificates using PAC-Bayes bounds and skeleton design.
result Achieves 77.0% coverage at 2% risk, outperforming baselines.
We show that Entropy-SGD (Chaudhari et al., 2017), when viewed as a learning algorithm, optimizes a PAC-Bayes bound on the risk of a Gibbs (posterior) classifier, i.e., a randomized classifier obtained by a risk-sensitive perturbation of the weights of a learned classifier. Entropy-SGD works by optimizing the bound's p…
Enhances normal mean estimation with side info using NIT approach.
problem Compound estimation of normal means with side information.
method Empirical Bayes, nonparametric integrative Tweedie (NIT) approach.
result NIT approach improves estimation risk and convergence rate with increasing auxiliary data.