21 research outputs found
An Exact Characterization of the Generalization Error for the Gibbs Algorithm
Various approaches have been developed to upper bound the generalization error of a supervised learning algorithm. However, existing bounds are often loose and lack of guarantees. As a result, they may fail to characterize the exact generalization ability of a learning algorithm.Our main contribution is an exact characterization of the expected generalization error of the well-known Gibbs algorithm (a.k.a. Gibbs posterior) using symmetrized KL information between the input training samples and the output hypothesis. Our result can be applied to tighten existing expected generalization error and PAC-Bayesian bounds. Our approach is versatile, as it also characterizes the generalization error of the Gibbs algorithm with data-dependent regularizer and that of the Gibbs algorithm in the asymptotic regime, where it converges to the empirical risk minimization algorithm. Of particular relevance, our results highlight the role the symmetrized KL information plays in controlling the generalization error of the Gibbs algorithm
Mutual information: a dependence measure for nonlinear time series
This paper investigates the possibility to analyse the structure of unconditional or conditional (and possibly nonlinear) dependence in financial returns without requiring the specification of mean-variance models or a theoretical probability distribution. The main goal of the paper is to show how mutual information can be used as a measure of dependence in financial time series. One major advantage of this approach resides precisely in its ability to account for nonlinear dependencies with no need to specify a theoretical probability distribution or use of a mean-variance model.Mutual information, nonlinear dependence, market efficiency
Information-Theoretic Characterizations of Generalization Error for the Gibbs Algorithm
Various approaches have been developed to upper
bound the generalization error of a supervised learning algorithm.
However, existing bounds are often loose and even vacuous when
evaluated in practice. As a result, they may fail to characterize
the exact generalization ability of a learning algorithm. Our
main contributions are exact characterizations of the expected
generalization error of the well-known Gibbs algorithm (a.k.a.
Gibbs posterior) using different information measures, in particular, the symmetrized KL information between the input training
samples and the output hypothesis. Our result can be applied to
tighten existing expected generalization errors and PAC-Bayesian
bounds. Our information-theoretic approach is versatile, as it also
characterizes the generalization error of the Gibbs algorithm with
a data-dependent regularizer and that of the Gibbs algorithm in
the asymptotic regime, where it converges to the standard empirical risk minimization algorithm. Of particular relevance, our
results highlight the role the symmetrized KL information plays
in controlling the generalization error of the Gibbs algorithm
Learning a model is paramount for sample efficiency in reinforcement learning control of PDEs
The goal of this paper is to make a strong point for the usage of dynamical
models when using reinforcement learning (RL) for feedback control of dynamical
systems governed by partial differential equations (PDEs). To breach the gap
between the immense promises we see in RL and the applicability in complex
engineering systems, the main challenges are the massive requirements in terms
of the training data, as well as the lack of performance guarantees. We present
a solution for the first issue using a data-driven surrogate model in the form
of a convolutional LSTM with actuation. We demonstrate that learning an
actuated model in parallel to training the RL agent significantly reduces the
total amount of required data sampled from the real system. Furthermore, we
show that iteratively updating the model is of major importance to avoid biases
in the RL training. Detailed ablation studies reveal the most important
ingredients of the modeling process. We use the chaotic Kuramoto-Sivashinsky
equation do demonstarte our findings