ContraBAR uses contrastive learning to learn Bayes-optimal policies in RL.
problem Learning optimal policies for unknown tasks sampled from a known distribution.
method Proposes ContraBAR, a meta RL algorithm using contrastive predictive coding (CPC) for belief inference.
result ContraBAR achieves comparable performance to state-of-the-art methods and is computationally efficient.
Memory-based models can learn to approximate Bayes-optimal predictors for non-stationary data.
problem Learning from non-stationary data with unobserved switching points.
method Memory-based neural models, including Transformers, LSTMs, and RNNs, trained to minimize log loss.
result Memory-based models can accurately approximate known Bayes-optimal algorithms and perform Bayesian inference over latent switching points.
Bayes-optimal limits in PCA with structured noise are determined.
problem Analyzing statistical dependencies in measurement noise for high-dimensional inference.
method Study of spiked matrix model with low-order polynomial orthogonal noise, providing Bayes-optimal limits and proposing a novel AMP.
result A novel AMP algorithm reaches the information-theoretic limits for more general priors.
BNRE improves simulation-based inference by producing more conservative posteriors.
problem Overconfident posteriors from current simulation-based inference algorithms risk false inferences.
method Balanced Neural Ratio Estimation (BNRE) that produces more conservative posterior approximations.
result BNRE produces more conservative posterior surrogates on all tested benchmarks and simulation budgets.
A method for Bayes-Adaptive Deep RL using meta-learning.
problem Maximizing expected return in unknown environments with uncertainty.
method variBAD: meta-learning for approximate inference and task uncertainty.
result variBAD achieves higher online return than existing methods in MuJoCo domains.
This study optimizes multi-modal learning thresholds and algorithms in high dimensions.
problem Optimizing multi-modal learning performance in high-dimensional data.
method Analytical quantification and derivation of AMP algorithm with state evolution analysis.
result Bayes-optimal performance and recovery thresholds derived for multi-modal data.
We analyse the matrix factorization problem. Given a noisy measurement of a product of two matrices, the problem is to estimate back the original matrices. It arises in many applications such as dictionary learning, blind matrix calibration, sparse principal component analysis, blind source separation, low rank matrix …
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…
Optimal classifiers derived from GMMs are approximated by deep neural networks.
problem Binary classification of high-dimensional overlapping Gaussian mixtures.
method Closed-form expressions for Bayes optimal decision boundaries derived from GMMs' eigenstructure. Empirical validation through synthetic and real-world data.
result Deep neural networks approximate optimal classifiers for GMMs, with decision thresholds related to covariance eigenvectors.
Meta-trained LSTM Meta-Learners learn tasks faster and differently than DL and RL systems.
problem Understanding the learning dynamics of meta-trained LSTM Meta-Learners compared to traditional DL and RL systems.
method Comparative analysis of learning trajectories on three structured tasks.
result Meta-trained LSTM Meta-Learners learn all task structure concurrently, unlike sample-inefficient DL and RL systems.
The paper tackles fair classification with multiple sensitive features.
problem Existing fair classification methods often consider a single sensitive feature, but in practice, individuals are defined by multiple sensitive features.
method Characterizes Bayes-optimal fair classifiers for multiple sensitive features under various fairness measures, proposing in-processing and post-processing algorithms.
result Bayes-optimal fair classifiers for multiple sensitive features are instance-dependent thresholding rules that rely on a weighted sum of group membership probabilities.
Unified framework for Bayes-optimal classifiers under group fairness.
problem Mitigating disparate impacts from algorithmic predictions in high-stakes decision-making.
method Unified framework based on Neyman-Pearson argument for deriving Bayes-optimal classifiers under group fairness constraints.
result Proposes FairBayes method that directly controls disparity and achieves optimal fairness-accuracy tradeoff.
Bayes-optimal learning of deep random networks with Gaussian weights is studied.
problem Learning a target function corresponding to a deep, extensive-width, non-linear neural network with random Gaussian weights.
method Closed-form expressions for Bayes-optimal test error, ridge regression, kernel and random features regression are computed.
result Optimally regularized ridge regression and kernel regression achieve Bayes-optimal performances, while logistic loss yields a near-optimal test error for classification.
Bayes-optimal classifiers are robust to adversarial attacks, unlike CNNs trained on the same data.
problem The vulnerability of modern CNN classifiers to adversarial examples.
method Constructing realistic image datasets and deriving analytic conditions for Bayes-optimal classifiers.
result Bayes-optimal classifiers are robust to adversarial attacks, unlike CNNs trained on the same data.
Paper finds optimal membership inference strategies for machine learning models.
problem Determining if a sample was part of the training set of a machine learning model.
method Derives optimal strategies for membership inference with assumptions on parameter distribution, showing that black-box attacks are as good as white-box attacks.
result Optimal strategies are not tractable, leading to approximations that outperform existing methods.
Bayes optimal algorithm under certain conditions doesn't achieve exponential simple regret.
problem Best arm identification with normal rewards over time.
method Fixed-budget best arm identification problem with rewards from normal distributions. Evaluates performance via simple regret.
result Bayes optimal algorithm does not yield exponential decrease in simple regret.
Study of Bayes optimal learning in high-dimensional linear regression with network side information.
problem Bayes optimal learning in high-dimensional linear regression with network side information.
method Introduce a Reg-Graph model and an iterative AMP algorithm for Bayes optimality under general conditions.
result Characterization of the limiting mutual information between latent signal and data observed.
The study analyzes multi-class teacher-student perceptron performance and generalization errors.
problem Analyzing multi-class classification with the teacher-student perceptron.
method Deriving asymptotic expressions for Bayes-optimal and empirical risk minimization (ERM) generalization errors.
result Regularised cross-entropy minimization yields close-to-optimal accuracy for multi-class classification.
Bayes-optimal learning of a neural network with quadratic activations is achieved with GAMP-RIE.
problem Learning a neural network with quadratic activations from quadratic samples.
method Combining approximate message passing with rotationally invariant matrix denoising.
result Derives a closed-form expression for Bayes-optimal test error.
Bayesian model averaging improves causal effect estimation by averaging over multiple models.
problem Estimating causal effects under linear Structural Causal Models (SCMs).
method Bayesian model averaging using Gaussian scale mixture distributions for computational efficiency.
result Bayesian model averaging is optimal for causal effect estimation.
Minimizes indecisions in selective classification to control misclassification rates.
problem Controlling misclassification rates in high-risk scenarios.
method Using indecisions to control misclassification rates, even below Bayes optimal.
result Control of misclassification rates to any user-specified level, even below Bayes optimal.
Unified approach for fair classification with overlapping groups.
problem Ensuring fairness across multiple overlapping groups in prediction problems.
method Probabilistic population analysis leading to Bayes-optimal classifier, unifying existing methods.
result Outperforms baselines in fairness-performance tradeoff on real datasets.
The paper proves statistical consistency and fairness guarantees for a plug-in algorithm.
problem Establishing statistical guarantees for fairness-aware binary classification.
method Proves statistical consistency and derives finite sample guarantees for the plug-in algorithm.
result The plug-in algorithm is statistically consistent and guarantees fairness and differential privacy.
Monte-Carlo Tree Search (MCTS) methods are drawing great interest after yielding breakthrough results in computer Go. This paper proposes a Bayesian approach to MCTS that is inspired by distributionfree approaches such as UCT [13], yet significantly differs in important respects. The Bayesian framework allows potential…
Develops methods for fair classification under linear disparity constraints.
problem Disparate impacts of machine learning algorithms on protected groups.
method Bayes-optimal fair classification methods via pre-, in-, and post-processing.
result Explicit forms of Bayes-optimal fair classifiers under linear disparity measures.
In statistical learning for real-world large-scale data problems, one must often resort to "streaming" algorithms which operate sequentially on small batches of data. In this work, we present an analysis of the information-theoretic limits of mini-batch inference in the context of generalized linear models and low-rank…
Study optimizes best-arm identification with minimax and Bayes strategies.
problem Efficiently identifying the best arm in fixed-budget scenarios.
method Adaptive procedure with two stages: pilot phase and minimax game.
result Single strategy is asymptotically minimax and Bayes optimal.
This paper tackles fair Bayes-optimal classifiers under predictive parity, proving their limitations and proposing a new algorithm.
problem Ensuring fair Bayes-optimal classifiers under predictive parity, especially when group performance levels vary widely.
method Proving the limitations of fair Bayes-optimal classifiers under predictive parity and proposing a new adaptive thresholding algorithm, FairBayes-DPP.
result Fair Bayes-optimal classifiers under predictive parity may not hold if group performance levels vary widely, leading to within-group unfairness.
Study on conditions for Bayes optimal classifier in adversarial robustness.
problem Existence of Bayes optimal classifier for adversarial robustness.
method General sufficient conditions for existence of Bayes optimal classifier.
result Guaranteed existence of Bayes optimal classifier under certain conditions.
Bayesian approach optimizes in-context learning for state space models.
problem Optimizing in-context learning for state space models.
method Bayesian optimal sequential prediction over latent sequence tasks.
result Bayesian optimal predictor converges to posterior predictive mean.
New framework shows cross-attention improves multi-modal in-context learning.
problem Understanding multi-modal in-context learning in neural networks.
method Mathematical framework and linearized cross-attention mechanism.
result Cross-attention mechanism is provably optimal for multi-modal in-context learning.
We consider effort allocation in crowdsourcing, where we wish to assign labeling tasks to imperfect homogeneous crowd workers to maximize overall accuracy in a continuous-time Bayesian setting, subject to budget and time constraints. The Bayes-optimal policy for this problem is the solution to a partially observable Ma…
AIM models explain deep learning in attention layers, offering solvable insights.
problem Understanding how deep learning models learn in attention layers.
method Statistical mechanics and random matrix theory.
result Closed-form predictions for Bayes-optimal generalization error and gradient descent performance.
Gradient-descent-based algorithms and their stochastic versions have widespread applications in machine learning and statistical inference. In this work we perform an analytic study of the performances of one of them, the Langevin algorithm, in the context of noisy high-dimensional inference. We employ the Langevin alg…
New method quantifies uncertainty for near-optimal ML algorithms.
problem Uncertainty quantification for near-Bayes optimal ML algorithms.
method Developed a martingale posterior to recover Bayesian posterior from ML algorithms.
result Proved practical uncertainty quantification method applicable to general ML algorithms.
Paper studies how few pretraining tasks are needed for a linear model to solve new tasks.
problem How many pretraining tasks are needed for a linear model to solve new tasks?
method Pretrained a linear attention model for linear regression with a Gaussian prior.
result Effective pretraining requires a small number of independent tasks, and the model closely matches Bayes optimal.
Paper presents ML-VAMP for efficient multi-layer inference with exact performance analysis.
problem Inference in multi-layer deep neural networks with non-convex optimization.
method ML-VAMP algorithm for MAP and MMSE estimates, with performance predictions in high dimensions.
result ML-VAMP achieves Bayes-optimal MSE under certain conditions, providing exact performance characterization.
Attention-only transformers learn from context via two stages of inference.
problem Learning from corrupted token sequences in minimal transformers.
method Two-stage empirical Bayes interpretation: kernel-weighted posterior mean and particle dynamics.
result Effective denoising without explicit noise schedules, showing posterior-mean recovery under asymptotic conditions.
Study exact limits of matrix reconstruction from noisy projections.
problem Reconstructing matrices from linear projections with high-dimensional data.
method Asymptotic analysis, universality properties, and generalized linear models.
result Exact asymptotic equations for optimal learning performance.
Paper establishes limits for accurately estimating low-rank matrices from noisy, non-linear data.
problem Estimating low-rank matrices from noisy, non-linear observations.
method Proves strong universality result with equivalent Gaussian model and effective prior parameters.
result Signal-to-noise ratio requirement grows as $N^{ rac 12 (1-1/k_F)}$ for accurate reconstruction.
The paper explores robust classifiers for imbalanced Gaussian data.
problem Adversarial robustness in machine learning with imbalanced data.
method Developed exact and approximate Bayes-optimal robust classifiers for Gaussian classification problems.
result Revealed fundamental tradeoffs between standard and robust accuracy.
Study of spiked matrix models with generative priors.
problem Performance enhancement in signal processing and statistical inference.
method Analysis of spiked matrix models with generative priors, using Bayes-optimal performance and enhanced spectral algorithms.
result Approximate message passing algorithm reaches optimal performance.
LDA-GO improves LDA for high-dimensional data via gradient optimization.
problem LDA struggles in high-dimensional settings due to unreliable covariance matrix estimation.
method LDA-GO learns a low-rank precision matrix via gradient optimization, automatically selecting between Gaussian likelihood and cross-entropy loss.
result LDA-GO outperforms other LDA variants in sparse-signal high-dimensional regimes.
Adaptive variational Bayes framework improves inference adaptively.
problem Lack of general and computationally tractable variational Bayes method for adaptive inference.
method Proposes a novel adaptive variational Bayes framework combining variational posteriors over individual models.
result Adaptive variational Bayes achieves optimal contraction rates adaptively under general conditions.
Sharp feature transitions revealed in extensive-width networks.
problem Learning hierarchical features from noisy queries in large networks.
method Information-theoretic analysis and heuristic decoupling argument.
result Sequential phase transitions in feature learnability and effective width.
Paper tackles regression with cost-based rejection, balancing prediction and rejection costs.
problem Regression with cost-based rejection, balancing prediction and rejection costs in a continuous target space.
method Formulated expected risk, derived Bayes optimal solution, proposed surrogate loss function.
result Bayes optimal solution can be recovered by the proposed surrogate loss function.
In many applications of black-box optimization, one can evaluate multiple points simultaneously, e.g. when evaluating the performances of several different neural network architectures in a parallel computing environment. In this paper, we develop a novel batch Bayesian optimization algorithm --- the parallel knowledge…
Study shows how classifiers can approach Bayes error in high-dimensional settings.
problem Generalization error in high-dimensional perceptrons.
method Proved a formula for generalization error using convex optimization and observed that logistic and hinge regression can approach Bayes error closely.
result Logistic and hinge regression can approach Bayes-optimal generalization error closely in high-dimensional settings.