Related papers: Rademacher complexity of stationary sequences
We construct data dependent bounds on the risk in function learning problems. The bounds are based on the local norms of the Rademacher process indexed by the underlying function class and they do not require prior knowledge about the…
We consider regression with square loss and general classes of functions without the boundedness assumption. We introduce a notion of offset Rademacher complexity that provides a transparent way to study localization both in expectation and…
Closed-loop performance of sequential decision making algorithms, such as model predictive control, depends strongly on the choice of controller parameters. Bayesian optimization allows learning of parameters from closed-loop experiments,…
Inspired from non-equilibrium statistical physics models, a general framework enabling the definition and synthesis of stationary time series with a priori prescribed and controlled joint distributions is constructed. Its central feature…
In modern interdisciplinary research, manifold time series data have been garnering more attention. A critical question in analyzing such data is ``stationarity'', which reflects the underlying dynamic behavior and is crucial across various…
We derive tests of stationarity for univariate time series by combining change-point tests sensitive to changes in the contemporary distribution with tests sensitive to changes in the serial dependence. The proposed approach relies on a…
We consider binary and multi-class classification problems using hypothesis classes of neural networks. For a given hypothesis class, we use Rademacher complexity estimates and direct approximation theorems to obtain a priori error…
Common practice in modern machine learning involves fitting a large number of parameters relative to the number of observations. These overparameterized models can exhibit surprising generalization behavior, e.g., ``double descent'' in the…
Finding interdependency relations between (possibly multivariate) time series provides valuable knowledge about the processes that generate the signals. Information theory sets a natural framework for non-parametric measures of several…
We study the sample complexity of learning neural networks, by providing new bounds on their Rademacher complexity assuming norm constraints on the parameter matrix of each layer. Compared to previous work, these complexity bounds have…
Performance estimation aims at estimating the loss that a predictive model will incur on unseen data. These procedures are part of the pipeline in every machine learning project and are used for assessing the overall generalisation ability…
Offset Rademacher complexities have been shown to provide tight upper bounds for the square loss in a broad class of problems including improper statistical learning and online learning. We show that the offset complexity can be generalized…
This paper is focused on the statistical analysis of data consisting of a collection of multiple series of probability measures that are indexed by distinct time instants and supported over a bounded interval of the real line. By modeling…
Relationships among time series can be exploited as inductive biases in learning effective forecasting models. In hierarchical time series, relationships among subsets of sequences induce hard constraints (hierarchical inductive biases) on…
This paper first establishes a strong law of large numbers and a strong invariance principle for forward and backward sums of near-epoch dependent sequences. Using these limiting theorems, we develop a general asymptotic theory on the Wald…
We propose a general framework for regularization in M-estimation problems under time dependent (absolutely regular-mixing) data which encompasses many of the existing estimators. We derive non-asymptotic concentration bounds for the…
The Model-free Prediction Principle of Politis (2015) has been successfully applied to general regression problems, as well as problems involving stationary time series. However, with long time series, e.g. annual temperature measurements…
We derive confidence intervals and confidence sequences for causal effects in situations where the back-door or front-door criteria are applicable. Our tightest confidence intervals hold in the standard setting where the training data…
Providing generalization guarantees for stochastic optimization algorithms remains a key challenge in learning theory. Recently, numerous works demonstrated the impact of the geometric properties of optimization trajectories on…
Deep neural networks (DNNs) have significantly advanced machine learning, with model depth playing a central role in their successes. The dynamical system modeling approach has recently emerged as a powerful framework, offering new…