New algorithm achieves data-dependent regret bounds in MDPs with unknown transitions.
problem Achieving best-of-both-worlds guarantees with data-dependent regret bounds in MDPs with unknown transitions.
method Optimistic follow-the-regularized-leader algorithm with new optimistic Q-function estimators and transition bonus.
result First-order, second-order, and path-length bounds with polylog(T) regret in the stochastic regime.
In this paper, we introduce a novel method to generate interpretable regression function estimators. The idea is based on called data-dependent coverings. The aim is to extract from the data a covering of the feature space instead of a partition. The estimator predicts the empirical conditional expectation over the cel…
In this work, we improve upon the stepwise analysis of noisy iterative learning algorithms initiated by Pensia, Jog, and Loh (2018) and recently extended by Bu, Zou, and Veeravalli (2019). Our main contributions are significantly improved mutual information bounds for Stochastic Gradient Langevin Dynamics via data-depe…
Reweighting improves risk bounds in certain data regions.
problem Improving risk bounds in classification and heteroscedastic regression.
method Weighted empirical risk minimization with a data-dependent weight function.
result A weighted ERM estimator can achieve superior performance in specific sub-regions.
New method reduces confidence interval sizes for causal inference.
problem Inaccurate propensity scores and extreme scores cause large confidence intervals.
method Data-dependent Coarse IPW (CIPW) estimators.
result Robust CIPW estimators reduce confidence interval sizes to ε+1/√n.
Improves normalizing flows by incorporating data dependencies.
problem Current normalizing flow learning assumes independent data, leading to errors.
method Proposes a likelihood objective with dependencies and efficient learning algorithm.
result Improves density estimation and data generation on real-world data.
We reformulate data-dependent constraints to ensure they are always met with high probability.
problem Ensuring fairness and stability in machine learning models with data-dependent constraints.
method Calibrated reformulation of constraints to guarantee satisfaction with a specified probability.
result Our method guarantees that fairness constraints are met at test time with high probability.
PriorGrad improves speech synthesis models by using data-dependent adaptive priors.
problem Inefficiency in denoising diffusion models due to mismatch between prior and data distributions.
method Proposes PriorGrad, an adaptive prior derived from data statistics based on conditional information.
result PriorGrad achieves faster convergence and superior performance in speech synthesis models.
We present a study of generalization for data-dependent hypothesis sets. We give a general learning guarantee for data-dependent hypothesis sets based on a notion of transductive Rademacher complexity. Our main result is a generalization bound for data-dependent hypothesis sets expressed in terms of a notion of hypothe…
PAC-Bayesian theory applied to data-dependent hypothesis sets yields uniform generalization bounds.
problem Proving uniform generalization bounds for data-dependent hypothesis sets.
method Applying PAC-Bayesian framework on 'random sets' and considering data-dependent hypothesis sets.
result Data-dependent uniform generalization bounds are proven, providing tighter and unified results.
The strategy of early stopping is a regularization technique based on choosing a stopping time for an iterative algorithm. Focusing on non-parametric regression in a reproducing kernel Hilbert space, we analyze the early stopping strategy for a form of gradient-descent applied to the least-squares loss function. We pro…
Differentially private method for estimating individualized treatment rules.
problem Estimating individualized treatment rules while preserving privacy.
method Differentially private two-stage empirical risk minimization (DP-2ERM).
result Improved privacy-utility trade-off demonstrated through simulations and applications.
In this paper we analyze a budgeted learning setting, in which the learner can only choose and observe a small subset of the attributes of each training example. We develop efficient algorithms for ridge and lasso linear regression, which utilize the geometry of the data by a novel data-dependent sampling scheme. When …
Optimal kernel in KR can be data-dependent, improving model performance.
problem Fixed kernel in KR limits model performance.
method Considered data-dependent kernels for KR, using posterior covariance.
result Data-dependent kernel choice leads to optimal performance.
In this paper, we present a novel way to summarize the structure of large graphs, based on non-parametric estimation of edge density in directed multigraphs. Following coclustering approach, we use a clustering of the vertices, with a piecewise constant estimation of the density of the edges across the clusters, and ad…
The paper improves PAC-Bayes bounds for data-dependent predictors.
problem Guaranteeing the quality of predictions on unseen examples.
method Basic PAC-Bayes inequality for stochastic kernels, leading to various bounds.
result Validates PAC-Bayes bounds without fixed 'data-free' priors and bounded losses.
Paper introduces data-dependent SSP for private linear and logistic regression.
problem Private linear and logistic regression with better performance.
method Data-dependent sufficient statistic perturbation (SSP) for linear and logistic regression.
result Data-dependent SSP outperforms state-of-the-art methods for linear and logistic regression.
The paper shows robustness and generalization are closely connected via data-dependent bounds.
problem Connecting robustness and generalization in machine learning.
method Data-dependent generalization bounds that reduce dependence on covering number and hypothesis space.
result Proves robustness implies generalization, with near-exponential improvements in various situations.
ST-BCP narrows the coverage gap in BCP by transforming nonconformity scores.
problem The looseness in BCP's coverage guarantee due to Markov's inequality.
method Introduces a data-dependent transformation of nonconformity scores.
result Reduces the average coverage gap from 4.20% to 1.12% on benchmarks.
In this dissertation we propose alternative analysis of distributed stochastic gradient descent (SGD) algorithms that rely on spectral properties of the data covariance. As a consequence we can relate questions pertaining to speedups and convergence rates for distributed SGD to the data distribution instead of the regu…
Paper analyzes trade-offs between fairness, privacy, and accuracy using Chernoff Information.
problem The relationship between fairness and privacy in machine learning.
method Utilizes Chernoff Information to characterize trade-offs, proposes Chernoff Difference and Noisy Chernoff Difference, develops CINE for neural estimation.
result Shows three distinct behaviors of Noisy Chernoff Difference based on data distribution.
The study improves representation learning bounds using data-dependent Gaussian mixtures.
problem Improving generalization in representation learning.
method Established bounds using relative entropy and MDL of latent variables.
result The approach significantly improves generalization over existing methods.
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.
The Probably Approximately Correct (PAC) Bayes framework (McAllester, 1999) can incorporate knowledge about the learning algorithm and (data) distribution through the use of distribution-dependent priors, yielding tighter generalization bounds on data-dependent posteriors. Using this flexibility, however, is difficult,…
A new learning method uses data to learn from large model sets.
problem Learning with large sets of candidate models where uniform convergence is hard.
method Data-dependent learning that incorporates empirical data less reliant on prior assumptions.
result Demonstrates improved generalization in various learning assumptions.
ZNMF improves facial recognition performance using data-dependent penalties.
problem Facial recognition performance in the Cambridge ORL database.
method ZNMF uses data-dependent auxiliary constraints to modify NMF.
result ZNMF outperforms other constrained NMF algorithms in facial recognition.
Paper introduces method to estimate animal motion on unknown submanifolds using Koopman operator.
problem Estimating animal motion on unknown submanifolds in high-dimensional space.
method Data-dependent approximation of Koopman operator in RKHS over ambient space.
result Strong rates of convergence derived for estimates in terms of fill distance.
Adaptive source selection for positive transfer in linear models improves target dataset performance.
problem Limited task-specific labeled data in business settings.
method Greedily decides from which sources and how many samples to incorporate into the target dataset using an accept/reject rule based on a data-dependent estimate of the transfer gain.
result Consistent gains over classical and recent strong baselines while avoiding negative transfer.
Survey on new data-dependent bounds for neural networks.
problem Generalization of overparameterized neural networks.
method Extending PAC-Bayesian theory, refining complexity terms, and replacing information-theoretic terms with stability assumptions.
result Unified template inequality and comparison of bounds.
Framework evaluates the impact of prior knowledge in deep learning models.
problem Mitigating data-driven model shortcomings like data dependence and generalization ability.
method Model-agnostic framework inspired by interpretable machine learning, assessing data volume and estimation range effects.
result Complex relationship between data and knowledge, including dependence, synergistic, and substitution effects.
Fast robust subspace tracking in sparse data-dependent noise with near-optimal delay.
problem Robustly tracking time-varying subspaces in the presence of sparse outliers.
method Introduces a fast mini-batch robust ST solution under mild assumptions.
result Provably correct subspace tracking with near-optimal delay and same time complexity as simple PCA.
A simple method for estimating PMF on large supports, preserving structure and suppressing noise.
problem Nonparametric estimation of multi-modal, heavy-tailed PMF on large discrete support.
method Data-dependent low-pass filtering on a line graph Laplacian.
result Smooth, multi-modal estimate of PMF that preserves coarse structure and suppresses noise.
We improve the robustness of Deep Neural Net (DNN) to adversarial attacks by using an interpolating function as the output activation. This data-dependent activation remarkably improves both the generalization and robustness of DNN. In the CIFAR10 benchmark, we raise the robust accuracy of the adversarially trained Res…
New algorithm learns changing discrete distributions with minimal drift error.
problem Learning discrete distributions that change over time with limited past samples.
method Adaptive algorithm using data-dependent bounds to balance statistical and drift errors.
result Tighter statistical error bounds for drifting distributions with or without finite support.
Enhances SDR via Hellinger correlation for better data dependency understanding.
problem Improving sufficient dimension reduction in single-index models.
method Developed a new method using Hellinger correlation for detecting the dimension reduction subspace.
result Significantly enhances and outperforms existing SDR methods through deeper data dependency understanding.
New algorithms reduce regret in online MDPs by adapting to data and variance.
problem Adapting to both adversarial and stochastic environments in online MDPs.
method Develops algorithms based on global optimization and policy optimization, using optimistic follow-the-regularized-leader with log-barrier regularization.
result Achieves refined data-dependent and variance-dependent regret bounds.
New approach for online learning with adaptive adversaries, simpler and more effective.
problem Online learning with adaptive adversaries, especially in bandits and MDPs.
method Uses standard unbiased estimators and a simple increasing learning rate schedule, aided by logarithmically homogeneous self-concordant barriers and strengthened Freedman's inequality.
result First high-probability regret bounds for adversarial bandits and MDPs, resolving open problems.
Estimates KRR risk from training data for various kernels and hyperparameters.
problem Predicting the generalization error of Kernel Ridge Regression.
method Introduces SCT and KARE to approximate KRR risk from training data.
result KARE provides an excellent approximation of KRR risk and helps select good kernels.
Paper establishes a generalization bound for gradient flow using a data-dependent kernel.
problem Understanding the generalization properties of gradient-based optimization methods.
method Establishes a generalization bound for gradient flow through a data-dependent kernel called the loss path kernel (LPK).
result The LPK captures the entire training trajectory and leads to tighter generalization guarantees.
PS-DME evaluates model performance and reliability after data-dependent selection.
problem Evaluating model performance and reliability when data is used for selection and evaluation.
method Post-selection distributional model evaluation (PS-DME) using e-values to control false coverage rate.
result PS-DME provides reliable comparison of model configurations across different reliability levels.
The clusters of a distribution are often defined by the connected components of a density level set. However, this definition depends on the user-specified level. We address this issue by proposing a simple, generic algorithm, which uses an almost arbitrary level set estimator to estimate the smallest level at which th…
In this paper, we consider the problem of prediction with expert advice in dynamic environments. We choose tracking regret as the performance metric and develop two adaptive and efficient algorithms with data-dependent tracking regret bounds. The first algorithm achieves a second-order tracking regret bound, which impr…
We present a general theoretical analysis of structured prediction with a series of new results. We give new data-dependent margin guarantees for structured prediction for a very wide family of loss functions and a general family of hypotheses, with an arbitrary factor graph decomposition. These are the tightest margin…
We present a Bayesian view of counterfactual risk minimization (CRM) for offline learning from logged bandit feedback. Using PAC-Bayesian analysis, we derive a new generalization bound for the truncated inverse propensity score estimator. We apply the bound to a class of Bayesian policies, which motivates a novel, pote…
New algorithm tackles multi-agent reinforcement learning with optimal convergence rate.
problem Multi-agent reinforcement learning with large state spaces and linear function approximations.
method Refined AVLPR framework with data-dependent pessimistic estimation and action-dependent bonuses.
result First algorithm with optimal O(T−1/2) convergence rate and no poly(Amax) dependency. This work obtains novel finite sample guarantees for Principal Component Analysis (PCA). These hold even when the corrupting noise is non-isotropic, and a part (or all of it) is data-dependent. Because of the latter, in general, the noise and the true data are correlated. The results in this work are a significant impr…
Combines linear and spectral estimators for signal recovery in generalized linear models.
problem Signal recovery from generalized linear models with Gaussian sensing matrix.
method Optimal combination of a linear estimator and a spectral estimator using an AMP algorithm.
result Bayes-optimal combination of estimators improves signal recovery.
Framework evaluates privacy cost of non-private pre-processing in DP pipelines.
problem Privacy cost of non-private data-dependent pre-processing in DP machine learning pipelines.
method Establishes upper bounds on overall privacy guarantees using Smooth DP and bounded sensitivity.
result Explicit overall privacy guarantees for various pre-processing algorithms.