Paper improves PAC-Bayes bounds for various loss types.
problem Improving PAC-Bayes bounds for different types of losses.
method Introducing new high-probability PAC-Bayes bounds for bounded and general tail behaviors losses, and extending to anytime-valid bounds.
result New fast-rate and mixed-rate bounds for losses with bounded ranges, and parameter-free bounds for losses with general tail behaviors.
Bounding shears in ideal triangulations on hyperbolic surfaces.
problem Bounding shears in ideal triangulations on hyperbolic surfaces.
method Showing an ideal triangulation with bounded shear parameters on hyperbolic surfaces.
result An upper bound on shear parameters depends logarithmically on the surface's topology.
New IDS algorithm refines parameter norm bounds for better bandit performance.
problem Frequentist IDS requires tight norm bounds, which are often unavailable in practice.
method Iteratively refines a high-probability upper bound on true parameter norm using data.
result Regret bounds independent of assumed parameter norm, outperforming state-of-the-art algorithms.
Paper refines PAC-Bayes bounds for bandit problems.
problem Improving probabilistic bounds for off-policy learning.
method Optimizes PAC-Bayesian bounds using a new parameter optimization approach.
result Provides two parameter-free PAC-Bayes bounds that nearly match optimal rates.
Lower bounds on private estimation of Gaussian covariance matrices.
problem Private estimation of Gaussian covariance matrices under various parameter regimes.
method Stein-Haff identity and fingerprinting lemma extensions.
result Lower bounds match existing upper bounds in the widest known parameters.
New method achieves optimal performance without needing problem parameters.
problem Parameter-free stochastic optimization in non-convex and convex settings.
method Simple hyperparameter search technique for non-convex setting, and method with stochastic gradients for convex setting.
result Fully parameter-free methods can outperform state-of-the-art algorithms in both non-convex and convex settings.
New bounds show current methods overestimate system parameter errors.
problem Current bounds overestimate parameter errors in system identification.
method Utilized asymptotic normality and second-order decomposition.
result Obtained finite-sample bounds matching optimal rates up to constants.
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.
FP-UCB algorithm achieves bounded regret for finitely parameterized multi-armed bandits.
problem Finitely parameterized multi-armed bandits with unknown but known parameter set.
method FP-UCB algorithm using structural information about the parameter set.
result FP-UCB achieves bounded regret under structural condition, logarithmic otherwise.
We consider a transfer-learning problem by using the parameter transfer approach, where a suitable parameter of feature mapping is learned through one task and applied to another objective task. Then, we introduce the notion of the local stability and parameter transfer learnability of parametric feature mapping,and th…
We give a simple optimistic algorithm for which it is easy to derive regret bounds of O ~ ( t m i x S A T ) \tilde{O}(\sqrt{t_{\rm mix} SAT}) O ~ ( t mix S A T ) after T T T steps in uniformly ergodic Markov decision processes with S S S states, A A A actions, and mixing time parameter t m i x t_{\rm mix} t mix . These bounds are the first regret bounds in the general, non-epi…
Computational limitations require more model parameters for robust learning.
problem Computational constraints affect the number of parameters needed for robust learning.
method Analyzes computational limitations and their impact on model size for robust learning.
result Computational bounded learners need significantly more parameters for robust learning.
New bounds on continuous random variables' right-tail probabilities.
problem Finding precise upper and lower limits for right-tail probabilities of continuous random variables.
method Developed new bounds based on PDF, first derivative, and two parameters.
result The new bounds are tight for various continuous random variables.
Sharp bounds on hyperbolic metrics in Ptolemaic spaces are derived.
problem Finding sharp bounds on hyperbolic metrics in Ptolemaic spaces.
method Construction of metrics on open subsets of Ptolemaic spaces.
result Sharp parameter bounds for hyperbolic and strongly hyperbolic metrics are derived.
The paper establishes bounds on the smoothness parameter in Gaussian process interpolation.
problem Estimating the smoothness parameter in Gaussian process models.
method Approximation theory in Sobolev spaces and general theorems on parameter estimation.
result Maximum likelihood estimation recovers the true smoothness for certain classes of functions.
Estimates matrix trace optimization with statistical learning theory.
problem Optimizing trace of parameter-dependent matrices.
method Monte Carlo estimator with bounds derived from epsilon nets and generic chaining.
result Predicts small sampling amount for matrices with small off-diagonal mass.
Algorithms often have tunable parameters that impact performance metrics such as runtime and solution quality. For many algorithms used in practice, no parameter settings admit meaningful worst-case bounds, so the parameters are made available for the user to tune. Alternatively, parameters may be tuned implicitly with…
The paper sets information-theoretic lower bounds for neural networks' parameter recovery and excess risk.
problem Establishing sample complexity lower bounds for neural network parameters and excess risk.
method Using information-theoretic tools, the paper proves lower bounds by constructing a generative network.
result Proves information-theoretic lower bounds for exact parameter recovery and positive excess risk.
New bounds on adaptivity cost in stochastic optimization.
problem Understanding the cost of changing strategies in stochastic optimization.
method Proving impossibility results for adaptivity in non-smooth stochastic convex optimization.
result Lower bounds on the price of adaptivity for different levels of uncertainty.
Improved DP SO with large Lipschitz parameters, handling outliers and heavy-tailed data.
problem Differential privacy in stochastic optimization with large Lipschitz parameters.
method Assumes bounded k-th order moments, provides linear-time algorithms for smooth convex and non-smooth convex losses.
result Improved risk bounds scaling with k-th moment, not uniform Lipschitz parameter.
Maxout networks study gradients and propose initialization strategies.
problem Complexity in input-output Jacobian distribution complicates stable parameter initialization.
method Obtained bounds on moments of gradients and formulated initialization strategies.
result Parameter initialization strategies improve training of deep maxout networks.
SGD-trained deep nets have bounds on their generalization error.
problem Bounding generalization error for deep neural networks trained by SGD.
method Combining dynamical control of parameter norms and Rademacher complexity estimates.
result Explicit bounds depend on loss trajectory, work for various architectures.
New insights into natural exponential families improve regret bounds for bandit problems.
problem Improving regret bounds for bandit problems with subexponential tails.
method Proving self-concordance for natural exponential families and applying to bandits.
result Optimistic algorithms for generalized linear bandits have second-order regret bounds that are free of an exponential dependence on problem parameters.
New method uses logical relations to derive bounds and inequality constraints from causal models.
problem Recovering bounds and inequality constraints from unobserved confounding.
method Using rules of probability and restrictions on counterfactuals implied by causal graphical models.
result Powerful method to recover known and novel bounds and constraints.
Develops a parameter-free SGD algorithm with optimal convergence rate.
problem Optimizing parameters in stochastic convex optimization.
method A novel parameter-free algorithm for SGD with high-probability guarantees and adaptive properties.
result Achieves optimal convergence rate with only a double-logarithmic factor increase compared to known-parameter settings.
We show that the log-likelihood of several probabilistic graphical models is Lipschitz continuous with respect to the lp-norm of the parameters. We discuss several implications of Lipschitz parametrization. We present an upper bound of the Kullback-Leibler divergence that allows understanding methods that penalize the …
Combinatorial dimensions play an important role in the theory of machine learning. For example, VC dimension characterizes PAC learning, SQ dimension characterizes weak learning with statistical queries, and Littlestone dimension characterizes online learning. In this paper we aim to develop combinatorial dimensions th…
New algorithms improve machine learning performance with explicit regret bounds.
problem Improving machine learning performance with explicit regret bounds.
method Projection-based linear regression algorithms with a focus on modern machine-learning models and their algorithmic performance.
result Established a priori regret bounds with explicit λ-dependence.
We address the problem of the achievable regret rates with online logistic regression. We derive lower bounds with logarithmic regret under L 1 L_1 L 1 , L 2 L_2 L 2 , and L ∞ L_\infty L ∞ constraints on the parameter values. The bounds are dominated by d / 2 log T d/2 \log T d /2 log T , where T T T is the horizon and d d d is the dimensionality of the parameter …
Study extends bounds on sample covariance matrices with general dependence.
problem Quantitative bounds on sample covariance matrices with i.i.d. columns.
method Extends previous work on deterministic equivalent to rectangular random matrices with general dependence structure.
result Proves quantitative bounds involving dimensions and spectral parameter, including closer proximity to real positive semi-line.
This paper improves GP-UCB by using a shifted exponential distribution for confidence parameters.
problem Theoretical confidence parameter in GP-UCB increases with iterations, leading to large values.
method Introduced IRGP-UCB, a randomized variant of GP-UCB using a shifted exponential distribution for confidence parameters.
result IRGP-UCB achieves sub-linear regret without increasing the confidence parameter.
Squint bound improved by removing ln ln T \ln \ln T ln ln T term.
problem Improving the Squint bound by removing the ln ln T \ln \ln T ln ln T term. method Using the Krichevsky--Trofimov algorithm to change the prior.
result Removed the ln ln T \ln \ln T ln ln T term from the Squint bound. Optimal ReLU networks can memorize any separable set of points with a small number of parameters.
problem The optimal number of parameters required to memorize a set of points using ReLU networks.
method Construction of ReLU networks with specific bit complexity to memorize points satisfying a mild separability assumption.
result Optimal ReLU networks can memorize any separable set of points with a number of parameters that is i l d e O ( N ) ilde{O}(\sqrt{N}) i l d e O ( N ) . 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.
Sharp bounds on ATE with unmeasured confounders, valid even when misspecified.
problem Bounding average treatment effects with unmeasured confounders.
method Distributionally robust optimization, double sharpness, double validity.
result Proposes estimators with robustness properties for valid bounds.
New bounds for shallow neural networks with deterministic parameters.
problem Developing generalisation bounds for shallow neural networks.
method PAC-Bayesian theory applied to shallow neural networks with deterministic parameters.
result Empirical non-vacuous bounds for shallow neural networks trained with vanilla SGD.
The study bounds the stability of Gaussian mixtures under small perturbations.
problem Stability of Gaussian mixtures under small changes in distribution.
method Deriving an explicit bound on parameter stability of spherical Gaussian Mixture Models (sGMM) in a pre-defined model class.
result Upper bound on parameter distance of close sGMMs to the original sGMM, dependent only on the original model.
Paper finds eigenvalue bounds for hyperbolic space domains.
problem Finding eigenvalue bounds for Robin Laplacian in hyperbolic space.
method Lower and upper bounds derived for eigenvalues.
result Geodesic ball maximizes eigenvalue in negative boundary parameter case.
Optimizes learning policies in average-reward MDPs with improved sample complexity.
problem Learning optimal policies in average-reward MDPs with limited samples.
method Reduces to discounted MDPs and uses improved bounds for variance parameters.
result Establishes minimax optimal sample complexity bound of O(SA(H/ε^2))
We show generalisation error bounds for deep learning with two main improvements over the state of the art. (1) Our bounds have no explicit dependence on the number of classes except for logarithmic factors. This holds even when formulating the bounds in terms of the L 2 L^2 L 2 -norm of the weight matrices, where previous bo…
We consider a variant of the classic multi-armed bandit problem where the expected reward of each arm is a function of an unknown parameter. The arms are divided into different groups, each of which has a common parameter. Therefore, when the player selects an arm at each time slot, information of other arms in the sam…
New method improves neural network robustness by identifying functions rather than parameters.
problem Neural networks' lack of robustness to distribution shifts.
method Identify the function represented by quadratic networks, not their parameters.
result Obtain robust generalization bounds for neural networks.
We introduce the Variational Holder (VH) bound as an alternative to Variational Bayes (VB) for approximate Bayesian inference. Unlike VB which typically involves maximization of a non-convex lower bound with respect to the variational parameters, the VH bound involves minimization of a convex upper bound to the intract…
Quantum reservoirs risk bounds are analyzed using Rademacher complexity.
problem Bounding generalization errors of quantum reservoirs.
method Using Rademacher complexity, specific bounds are derived for quantum reservoir classes.
result Risk bounds converge with increasing training samples and qubits.
Careful tuning of a regularization parameter is indispensable in many machine learning tasks because it has a significant impact on generalization performances. Nevertheless, current practice of regularization parameter tuning is more of an art than a science, e.g., it is hard to tell how many grid-points would be need…
The paper examines utility maximization in markets with hidden Gaussian drift, finding restrictions on model parameters.
problem Utility maximization problems in markets with hidden Gaussian drift mean-reverting processes.
method Derives sufficient conditions for bounded maximum expected utility of terminal wealth for models with full and partial information.
result Restrictions on model parameters for bounded maximum expected utility.
Bayesian optimisation has gained great popularity as a tool for optimising the parameters of machine learning algorithms and models. Somewhat ironically, setting up the hyper-parameters of Bayesian optimisation methods is notoriously hard. While reasonable practical solutions have been advanced, they can often fail to …
Improved bounds on neural network regions using activation histograms.
problem Bounding the number of affine regions in ReLU networks.
method Analysis of algebraic topology problem, extension of framework to subnetwork composition.
result Slightly tighter bounds and insights into parameter initialization.