Related papers: Optimal Piecewise Local-Linear Approximations

Local Interpretable Model-Agnostic Explanations (LIME) is a popular method to perform interpretability of any kind of Machine Learning (ML) model. It explains one ML prediction at a time, by learning a simple linear model around the…

Interpretability methods are developed to understand the working mechanisms of black-box models, which is crucial to their responsible deployment. Fulfilling this goal requires both that the explanations generated by these methods are…

Reliably predicting the behavior of language models -- such as whether their outputs are correct or have been adversarially manipulated -- is a fundamentally challenging task. This is often made even more difficult as frontier language…

Aiming for accurate estimation of system reliability of load-sharing systems, a flexible model for such systems is constructed by approximating the cumulative hazard functions of component lifetimes using piecewise linear functions. The…

Most of the work on interpretable machine learning has focused on designing either inherently interpretable models, which typically trade-off accuracy for interpretability, or post-hoc explanation systems, which lack guarantees about their…

Despite the wide use of explainability techniques to attempt to understand the behavior of Artificial Intelligence (AI), the generated explanations may not always be reliable. An explanation can appear plausible to humans but fail to…

In this paper we aim to construct piecewise-linear (PWL) approximations for functions of multiple variables and to build compact mixed-integer linear programming (MILP) formulations to represent the resulting PWL function. On the one hand,…

With dramatic improvements in optimization software, the solution of large-scale problems that seemed intractable decades ago are now a routine task. This puts even more real-world applications into the reach of optimizers. At the same…

High-dimensional black-box optimisation remains an important yet notoriously challenging problem. Despite the success of Bayesian optimisation methods on continuous domains, domains that are categorical, or that mix continuous and…

Motivated by the problem of tuning hyperparameters in machine learning, we present a new approach for gradually and adaptively optimizing an unknown function using estimated gradients. We validate the empirical performance of the proposed…

Bayesian optimization is a coherent, ubiquitous approach to decision-making under uncertainty, with applications including multi-arm bandits, active learning, and black-box optimization. Bayesian optimization selects decisions (i.e.…

In this contribution we present a survey of concepts in localized model order reduction methods for parameterized partial differential equations. The key concept of localized model order reduction is to construct local reduced spaces that…

The financial industry faces a significant challenge modeling and risk portfolios: balancing the predictability of advanced machine learning models, neural network models, and explainability required by regulatory entities (such as Office…

Nowadays, deep neural networks are being used in many domains because of their high accuracy results. However, they are considered as "black box", means that they are not explainable for humans. On the other hand, in some tasks such as…

Many mathematical modelling tasks (such as in Economics and Finance) are informed by data that is "found" rather than being the result of carefully designed experiments. This often results in data series that are short, noisy,…

We establish efficient approximate counting algorithms for several natural problems in local lemma regimes. In particular, we consider the probability of intersection of events and the dimension of intersection of subspaces. Our approach is…

As the use of deep learning techniques has grown across various fields over the past decade, complaints about the opaqueness of the black-box models have increased, resulting in an increased focus on transparency in deep learning models.…

We consider the problem of designing piecewise affine policies for two-stage adjustable robust linear optimization problems under right-hand side uncertainty. It is well known that a piecewise affine policy is optimal although the number of…

We propose a black-box approach to reducing large semidefinite programs to a set of smaller semidefinite programs by projecting to random linear subspaces. We evaluate our method on a set of polynomial optimization problems, demonstrating…

The complex nature of lithium-ion battery degradation has led to many machine learning based approaches to health forecasting being proposed in literature. However, machine learning can be computationally intensive. Linear approaches are…