Data availability has dramatically increased in recent years, driving model-based control methods to exploit learning techniques for improving the system description, and thus control performance. Two key factors that hinder the practical applicability of learning methods in control are their high computational complexity and limited generalization capabilities to unseen conditions. Meta-learning is a powerful tool that enables efficient learning across a finite set of related tasks, easing adaptation to new unseen tasks. This paper makes use of a meta-learning approach for adaptive model predictive control, by learning a system model that leverages data from previous related tasks, while enabling fast fine-tuning to the current task during closed-loop operation. The dynamics is modeled via Gaussian process regression and, building on the Karhunen-Lo{\`e}ve expansion, can be approximately reformulated as a finite linear combination of kernel eigenfunctions. Using data collected over a set of tasks, the eigenfunction hyperparameters are optimized in a meta-training phase by maximizing a variational bound for the log-marginal likelihood. During meta-testing, the eigenfunctions are fixed, so that only the linear parameters are adapted to the new unseen task in an online adaptive fashion via Bayesian linear regression, providing a simple and efficient inference scheme. Simulation results are provided for autonomous racing with miniature race cars adapting to unseen road conditions.

The paper covers the design and analysis of experiments to discriminate between two Gaussian process models, such as those widely used in computer experiments, kriging, sensor location and machine learning. Two frameworks are considered. First, we study sequential constructions, where successive design (observation) points are selected, either as additional points to an existing design or from the beginning of observation. The selection relies on the maximisation of the difference between the symmetric Kullback Leibler divergences for the two models, which depends on the observations, or on the mean squared error of both models, which does not. Then, we consider static criteria, such as the familiar log-likelihood ratios and the Fr\'echet distance between the covariance functions of the two models. Other distance-based criteria, simpler to compute than previous ones, are also introduced, for which, considering the framework of approximate design, a necessary condition for the optimality of a design measure is provided. The paper includes a study of the mathematical links between different criteria and numerical illustrations are provided.

Most models in machine learning contain at least one hyperparameter to control for model complexity. Choosing an appropriate set of hyperparameters is both crucial in terms of model accuracy and computationally challenging. In this work we propose an algorithm for the optimization of continuous hyperparameters using inexact gradient information. An advantage of this method is that hyperparameters can be updated before model parameters have fully converged. We also give sufficient conditions for the global convergence of this method, based on regularity conditions of the involved functions and summability of errors. Finally, we validate the empirical performance of this method on the estimation of regularization constants of L2-regularized logistic regression and kernel Ridge regression. Empirical benchmarks indicate that our approach is highly competitive with respect to state of the art methods.

We introduce Sequential Neural Posterior Score Estimation (SNPSE) and Sequential Neural Likelihood Score Estimation (SNLSE), two new score-based methods for Bayesian inference in simulator-based models. Our methods, inspired by the success of score-based methods in generative modelling, leverage conditional score-based diffusion models to generate samples from the posterior distribution of interest. These models can be trained using one of two possible objective functions, one of which approximates the score of the intractable likelihood, while the other directly estimates the score of the posterior. We embed these models into a sequential training procedure, which guides simulations using the current approximation of the posterior at the observation of interest, thereby reducing the simulation cost. We validate our methods, as well as their amortised, non-sequential variants, on several numerical examples, demonstrating comparable or superior performance to existing state-of-the-art methods such as Sequential Neural Posterior Estimation (SNPE) and Sequential Neural Likelihood Estimation (SNLE).

Learning from data has led to substantial advances in a multitude of disciplines, including text and multimedia search, speech recognition, and autonomous-vehicle navigation. Can machine learning enable similar leaps in the natural and social sciences? This is certainly the expectation in many scientific fields and recent years have seen a plethora of applications of non-linear models to a wide range of datasets. However, flexible non-linear solutions will not always improve upon manually adding transforms and interactions between variables to linear regression models. We discuss how to recognize this before constructing a data-driven model and how such analysis can help us move to intrinsically interpretable regression models. Furthermore, for a variety of applications in the natural and social sciences we demonstrate why improvements may be seen with more complex regression models and why they may not.

Hyperparameter tuning, any machine learning model training activity needs to be optimised. The learning process cannot extract the hyperparameters of a model from the provided datasets. However, they are extremely important for managing the actual learning process. These hyperparameters are derived from how machine learning models are mathematically formulated. For instance, while the learning rate in gradient descent is a parameter, the weights learned during the training of a linear regression model are parameters.

Build a solid foundation in Machine Learning: Linear Regression, Logistic Regression and K-Means Clustering in Python

In this paper, we address the challenge of performing counterfactual inference with observational data via Bayesian nonparametric regression adjustment, with a focus on high-dimensional settings featuring multiple actions and multiple correlated outcomes. We present a general class of counterfactual multi-task deep kernels models that estimate causal effects and learn policies proficiently thanks to their sample efficiency gains, while scaling well with high dimensions. In the first part of the work, we rely on Structural Causal Models (SCM) to formally introduce the setup and the problem of identifying counterfactual quantities under observed confounding. We then discuss the benefits of tackling the task of causal effects estimation via stacked coregionalized Gaussian Processes and Deep Kernels. Finally, we demonstrate the use of the proposed methods on simulated experiments that span individual causal effects estimation, off-policy evaluation and optimization.

Graph contrastive learning (GCL) emerges as the most representative approach for graph representation learning, which leverages the principle of maximizing mutual information (InfoMax) to learn node representations applied in downstream tasks. To explore better generalization from GCL to downstream tasks, previous methods heuristically define data augmentation or pretext tasks. However, the generalization ability of GCL and its theoretical principle are still less reported. In this paper, we first propose a metric named GCL-GE for GCL generalization ability. Considering the intractability of the metric due to the agnostic downstream task, we theoretically prove a mutual information upper bound for it from an information-theoretic perspective. Guided by the bound, we design a GCL framework named InfoAdv with enhanced generalization ability, which jointly optimizes the generalization metric and InfoMax to strike the right balance between pretext task fitting and the generalization ability on downstream tasks. We empirically validate our theoretical findings on a number of representative benchmarks, and experimental results demonstrate that our model achieves state-of-the-art performance.

Here I would like to provide some useful machine-learning algorithms you should know. Machine learning is a branch of Artificial Intelligence that enables computers to learn and make predictions based on data. Traditional AI focuses on programming computers to perform specific tasks, such as playing chess or recognizing faces. Machine learning is about giving computers the ability to learn new things and solve new problems without being explicitly programmed. If you are reading this article, you might be one of those curious souls who asks'what if' questions and likes puzzles.