This paper improves meta-learning by developing new PAC-Bayes bounds.
problem Meta-learning generalization gap across multiple tasks.
method Upper bounding convex functions linking environment and task-level losses.
result New PAC-Bayes bounds for meta-learning with improved algorithms.
New empirical PAC-Bayes bound for Markov chains with finite state space.
problem Lack of empirical bounds for Markov chains with temporal dependence.
method Proved a new PAC-Bayes bound for Markov chains, providing an empirical pseudo-spectral gap.
result First fully empirical PAC-Bayes bound for Markov chains with finite state space.
New bounds show limitations of sample-wise information-theoretic generalization.
problem Limitations of sample-wise information-theoretic generalization bounds.
method Analysis of existing bounds and derivation of new bounds.
result No sample-wise information-theoretic bounds exist for expected squared generalization gap.
The paper proves how Transformers learn from context and generalize well.
problem Understanding how Transformers generalize from diverse tasks.
method Developed a statistical theory for in-context learning, separating risk into Bayes Gap and Posterior Variance.
result The Posterior Variance is task-independent, and the Bayes Gap decreases with more in-context examples.
Derandomizing PAC-Bayes bounds for smooth loss functions
problem Derandomizing PAC-Bayes bounds for smooth loss functions
method Exploiting smoothness properties of both the loss and the predictor class
result Bounds for deterministic predictors that involve flatness quantities
New complexity measure explains neural network generalization gap.
problem Understanding the generalization gap between neural networks and linear models.
method Introducing a new complexity measure for functions that governs PAC-Bayes bounds and relates to neural network complexity.
result Demonstrates a separation in sample complexity between 2 and 4-layer neural networks for periodic functions.
New analysis reveals gaps in selective classifiers, guiding improvements.
problem Improving selective classifiers to match perfect-ordering oracle performance.
method Formalized selective classification gap, decomposed into five sources of looseness.
result Monotone post-hoc calibration has limited impact on closing the gap.
Researchers estimate optimal PAC-Bayes bounds using Hamiltonian Monte Carlo.
problem Estimating tight PAC-Bayes bounds with restricted posterior families.
method Sampling from optimal Gibbs posterior using Hamiltonian Monte Carlo, estimating KL divergence, and proposing high-probability bounds.
result Significant tightness gaps in PAC-Bayes bounds, up to 5-6% in some cases.
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.
PAC-Bayes bound for stable RNNs in time-series data.
problem Bounding generalization gap for stable RNNs in time-series data.
method Derived a PAC-Bayes bound with stability constraints for discrete-time non-linear dynamical systems, including stable RNNs.
result The bound converges to zero as dataset size increases, and does not grow with RNN steps.
Paper develops a new generalization bound using PAC-Bayes theory and Gibbs distributions.
problem Limits of traditional generalization bounds due to complexity measures.
method Leverages PAC-Bayes bounds with Gibbs distributions to derive a flexible generalization bound.
result Derives a generalization bound that can adapt to both hypothesis class and task complexity.
Derives bounds for deterministic predictors using smooth loss functions.
problem Generalizing probabilistic predictors to deterministic ones.
method Exploits smoothness properties of loss and predictor classes, controlling the Jensen gap class through Rademacher complexity.
result Derives bounds for deterministic predictors involving flatness quantities from Jacobians and Hessians.
Due to its linear complexity, naive Bayes classification remains an attractive supervised learning method, especially in very large-scale settings. We propose a sparse version of naive Bayes, which can be used for feature selection. This leads to a combinatorial maximum-likelihood problem, for which we provide an exact…
In this draft, which reports on work in progress, we 1) adapt the information bottleneck functional by replacing the compression term by class-conditional compression, 2) relax this functional using a variational bound related to class-conditional disentanglement, 3) consider this functional as a training objective for…
Improves Bayesian predictive performance in misspecified models.
problem Misspecification gap between inferential and predictive risks.
method Develops a multi-sample loss (PACm) to bridge the gap. result Empirical study shows improved predictive distribution.
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.
New method calibrates machine learning models with theoretical guarantees.
problem Lack of theoretical guarantees for recalibration in multiclass classification.
method PAC-Bayes analysis for generalization error in calibration.
result First optimizable upper bound for generalization error in calibration.
Deep neural networks are optimal for dependent data using PAC-Bayes bounds.
problem Optimizing deep neural networks for dependent data.
method PAC-Bayes oracle inequalities and Bernstein inequality.
result Upper and lower bounds match, proving minimax optimality.
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…
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.
Bayes-consistent disagreement discrepancy loss improves model robustness.
problem Distribution shift in real-world neural network deployment.
method Introducing a novel disagreement loss that is Bayes consistent.
result Proves existing surrogates for disagreement discrepancy are not Bayes consistent.
Study improves theoretical understanding of Bayesian deep learning for classification tasks.
problem Theoretical gap in understanding Bayesian approaches in deep learning for classification.
method PAC-Bayes bounds techniques and Spike-and-Slab priors for sparse deep learning.
result Established non-asymptotic results for prediction error, achieving minimax optimal rates.
New PAC-Bayesian bounds explain few-shot learning performance gaps.
problem Gap between PAC-Bayesian theory and practice in few-shot learning.
method Developed new PAC-Bayesian bounds for few-shot learning, derived MAML and Reptile from these bounds, and introduced a new PACMAML algorithm.
result PAC-Bayesian bounds explain performance of MAML and Reptile, and outperform existing algorithms.
Random projections improve classifier generalization without needing to choose the best threshold.
problem Improving classifier generalization without choosing the best threshold.
method Thresholding a random one-dimensional feature after random projection of data.
result Generalization gap is significantly smaller than linear classifiers.
Understanding generalization in reinforcement learning (RL) is a significant challenge, as many common assumptions of traditional supervised learning theory do not apply. We focus on the special class of reparameterizable RL problems, where the trajectory distribution can be decomposed using the reparametrization trick…
A new framework integrates classification and regression tasks in multi-task learning.
problem Jointly solving classification and regression tasks in multi-task scenarios.
method Two-Stage Learning-to-Defer (L2D) framework with a unified deferral mechanism.
result Unified deferral mechanism ensures convergence to the Bayes-optimal rejector.
The CAP slope is Bayes' theorem in cumulative coordinates, unlocking the weight of evidence, Somers' D, and Gini coefficient.
problem Calibration and weight of evidence
method Identifying the CAP slope as Bayes' theorem
result Revealing the CAP slope as Bayes' theorem
IIC provides a PAC-Bayes bound for interpolating models, revealing factors affecting generalization.
problem Theoretical challenges in understanding overparameterized models and their performance.
method PAC-Bayesian perspective applied to the Interpolating Information Criterion (IIC).
result Test error for overparameterized models achieving zero training error depends on various factors.
Robust VB framework for large datasets with outliers.
problem Handling outliers and contamination in large datasets.
method Divide and conquer approach with geometric median aggregation.
result VM-Posterior distribution preserves contraction properties.
Transformer attention layers solve single-location regression tasks.
problem Understanding token-wise sparsity and internal linear representations in attention-based models.
method Introduce single-location regression task and a simplified predictor based on self-attention layers.
result Transformer attention layers are asymptotically Bayes optimal and can learn underlying structures effectively.
Study on limits of LLM-based multi-agent planning reliability.
problem Reliability limits of LLM-based multi-agent planning.
method Modeling LLM-based multi-agent architecture as a decision network, showing dominance by centralized Bayes decision maker.
result Optimizing multi-agent directed acyclic graphs under communication budget is equivalent to choosing a constrained experiment.
The paper establishes bounds for transductive learning using information theory.
problem Transductive learning generalization gap control.
method Information theory, PAC-Bayes, mutual information, conditional mutual information, different information measures.
result Established transductive information-theoretic and PAC-Bayesian bounds.
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.
New bounds for Bayesian bandits show prior improves performance.
problem Improving regret bounds for Bayesian bandits.
method Upper confidence bound algorithm with finite-time logarithmic regret bounds.
result Derives O(cΔlogn) and O(chlog2n) upper bounds for Bayesian bandits. Given a graph in which a few vertices are deemed interesting a priori, the vertex nomination task is to order the remaining vertices into a nomination list such that there is a concentration of interesting vertices at the top of the list. Previous work has yielded several approaches to this problem, with theoretical re…
Deep ensembles mimic Bayesian averaging with learned priors.
problem Quantifying uncertainty in neural networks.
method Showed deep ensembles perform exact Bayesian averaging with an implicitly learned data-dependent prior.
result Deep ensembles are Bayesian and provide an explanation for their strong empirical performance.
New uniqueness concept for adversarial Bayes classifier.
problem Understanding adversarial Bayes classifiers in binary classification.
method Developed a new notion of uniqueness and analyzed it for a family of one-dimensional data distributions.
result Improved regularity of adversarial Bayes classifiers as perturbation radius increases.
Study optimal algorithms for recovering signals through inhomogeneous low-rank channels.
problem Recovering signals through an inhomogeneous low-rank matrix channel.
method Derive and analyze an approximate message-passing algorithm (AMP) and a spectral method.
result The AMP iteration matches the conjectured optimal computational phase transition.
Empirical Bayes rates via variational approximations and prior decomposition.
problem Nonparametric and high-dimensional inference convergence rates.
method Variational perspective and prior decomposition.
result Empirical Bayes posterior rates derived from variational Bayes.
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.
In this paper, we consider the nonparametric least square regression in a Reproducing Kernel Hilbert Space (RKHS). We propose a new randomized algorithm that has optimal generalization error bounds with respect to the square loss, closing a long-standing gap between upper and lower bounds. Moreover, we show that our al…
Despite its simplicity, the naive Bayes classifier has surprised machine learning researchers by exhibiting good performance on a variety of learning problems. Encouraged by these results, researchers have looked to overcome naive Bayes primary weakness - attribute independence - and improve the performance of the algo…
Conventional research attributes the improvements of generalization ability of deep neural networks either to powerful optimizers or the new network design. Different from them, in this paper, we aim to link the generalization ability of a deep network to optimizing a new objective function. To this end, we propose a \…
Researchers prove NP-hardness of learning parameter-bounded Bayes nets.
problem Learning parameter-bounded Bayes nets is computationally hard.
method Proved NP-hardness of learning parameter-bounded Bayes nets and a promise search variant.
result Proved NP-hardness of a promise search variant of LEARN.
Deep learning improves Bayes factor computation for likelihood-free models.
problem Computing Bayes factors for likelihood-free models is challenging.
method Proposes a deep learning estimator of Bayes factors using simulated data.
result Establishes consistency of the Deep Bayes Factor estimator.
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.
PAC-Bayes framework fails on simple 1D linear classification task.
problem Proving the learnability of simple 1D linear classification tasks using PAC-Bayes bounds.
method Demonstrated a specific 1D linear classification task that PAC-Bayes cannot analyze.
result PAC-Bayes framework cannot prove learnability of simple 1D linear classification tasks.
We consider the problem of Gaussian mixture clustering in the high-dimensional limit where the data consists of m points in n dimensions, n,m→∞ and α=m/n stays finite. Using exact but non-rigorous methods from statistical physics, we determine the critical value of α and the distance between…