arXiv research

Paper improves PAC-Bayes bounds for various loss types.

Bounding shears in ideal triangulations on hyperbolic surfaces.

New IDS algorithm refines parameter norm bounds for better bandit performance.

Paper refines PAC-Bayes bounds for bandit problems.

Lower bounds on private estimation of Gaussian covariance matrices.

New method achieves optimal performance without needing problem parameters.

New bounds show current methods overestimate system parameter errors.

Researchers prove NP-hardness of learning parameter-bounded Bayes nets.

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 $\tilde{O}(\sqrt{t_{\rm mix} SAT})$ after $T$ steps in uniformly ergodic Markov decision processes with $S$ states, $A$ actions, and mixing time parameter $t_{\rm mix}$. These bounds are the first regret bounds in the general, non-epi…

Computational limitations require more model parameters for robust learning.

New bounds on continuous random variables' right-tail probabilities.

Sharp bounds on hyperbolic metrics in Ptolemaic spaces are derived.

The paper establishes bounds on the smoothness parameter in Gaussian process interpolation.

Estimates matrix trace optimization with statistical learning theory.

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.

New bounds on adaptivity cost in stochastic optimization.

Improved DP SO with large Lipschitz parameters, handling outliers and heavy-tailed data.

Maxout networks study gradients and propose initialization strategies.

SGD-trained deep nets have bounds on their generalization error.

New insights into natural exponential families improve regret bounds for bandit problems.

New method uses logical relations to derive bounds and inequality constraints from causal models.

Develops a parameter-free SGD algorithm with optimal convergence rate.

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 …

We consider the problem of finitely parameterized multi-armed bandits where the model of the underlying stochastic environment can be characterized based on a common unknown parameter. The true parameter is unknown to the learning agent. However, the set of possible parameters, which is finite, is known a priori. We pr…

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.

We address the problem of the achievable regret rates with online logistic regression. We derive lower bounds with logarithmic regret under $L_1$, $L_2$, and $L_\infty$ constraints on the parameter values. The bounds are dominated by $d/2 \log T$, where $T$ is the horizon and $d$ is the dimensionality of the parameter …

Study extends bounds on sample covariance matrices with general dependence.

This paper improves GP-UCB by using a shifted exponential distribution for confidence parameters.

Squint bound improved by removing $\ln \ln T$ term.

Optimal ReLU networks can memorize any separable set of points with a small number of parameters.

Lower bounds on Bayes risk for realizable models derived using information theory.

Sharp bounds on ATE with unmeasured confounders, valid even when misspecified.

New bounds for shallow neural networks with deterministic parameters.

The study bounds the stability of Gaussian mixtures under small perturbations.

Paper finds eigenvalue bounds for hyperbolic space domains.

Optimizes learning policies in average-reward MDPs with improved sample complexity.

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 $L^2$-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.

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.

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.

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.