Causal effect estimation seeks to determine the impact of an intervention from observational data. However, the existing causal inference literature primarily addresses treatment effects on frequently occurring events. But what if we are interested in estimating the effects of a policy intervention whose benefits, while potentially important, can only be observed and measured in rare yet impactful events, such as extreme climate events? The standard causal inference methodology is not designed for this type of inference since the events of interest may be scarce in the observed data and some degree of extrapolation is necessary. Extreme Value Theory (EVT) provides methodologies for analyzing statistical phenomena in such extreme regimes. We introduce a novel framework for assessing treatment effects in extreme data to capture the causal effect at the occurrence of rare events of interest. In particular, we employ the theory of multivariate regular variation to model extremities. We develop a consistent estimator for extreme treatment effects and present a rigorous non-asymptotic analysis of its performance. We illustrate the performance of our estimator using both synthetic and semi-synthetic data.

Analog electrical networks have long been investigated as energy-efficient computing platforms for machine learning, leveraging analog physics during inference. More recently, resistor networks have sparked particular interest due to their ability to learn using local rules (such as equilibrium propagation), enabling potentially important energy efficiency gains for training as well. Despite their potential advantage, the simulations of these resistor networks has been a significant bottleneck to assess their scalability, with current methods either being limited to linear networks or relying on realistic, yet slow circuit simulators like SPICE. Assuming ideal circuit elements, we introduce a novel approach for the simulation of nonlinear resistive networks, which we frame as a quadratic programming problem with linear inequality constraints, and which we solve using a fast, exact coordinate descent algorithm. Our simulation methodology significantly outperforms existing SPICE-based simulations, enabling the training of networks up to 327 times larger at speeds 160 times faster, resulting in a 50,000-fold improvement in the ratio of network size to epoch duration. Our approach can foster more rapid progress in the simulations of nonlinear analog electrical networks.

A key task in actuarial modelling involves modelling the distributional properties of losses. Classic (distributional) regression approaches like Generalized Linear Models (GLMs; Nelder and Wedderburn, 1972) are commonly used, but challenges remain in developing models that can (i) allow covariates to flexibly impact different aspects of the conditional distribution, (ii) integrate developments in machine learning and AI to maximise the predictive power while considering (i), and, (iii) maintain a level of interpretability in the model to enhance trust in the model and its outputs, which is often compromised in efforts pursuing (i) and (ii). We tackle this problem by proposing a Distributional Refinement Network (DRN), which combines an inherently interpretable baseline model (such as GLMs) with a flexible neural network-a modified Deep Distribution Regression (DDR; Li et al., 2019) method. Inspired by the Combined Actuarial Neural Network (CANN; Schelldorfer and W{\''u}thrich, 2019), our approach flexibly refines the entire baseline distribution. As a result, the DRN captures varying effects of features across all quantiles, improving predictive performance while maintaining adequate interpretability. Using both synthetic and real-world data, we demonstrate the DRN's superior distributional forecasting capacity. The DRN has the potential to be a powerful distributional regression model in actuarial science and beyond.

Generative modeling has drawn much attention in creative and scientific data generation tasks. Score-based Diffusion Models, a type of generative model that iteratively learns to denoise data, have shown state-of-the-art results on tasks such as image generation, multivariate time series forecasting, and robotic trajectory planning. We further analyze the model's ability to learn the characteristics of the original dataset and its ability to produce transfers that follow the underlying dynamics. Ablation studies were conducted to determine how model performance varies with model size and trajectory temporal resolution. In addition, a performance benchmark is designed to assess the generative model's usefulness for trajectory design, conduct model performance comparisons, and lay the groundwork for evaluating different generative models for trajectory design beyond diffusion. The results of this analysis showcase several useful properties of diffusion models that, when taken together, can enable a future system for generative trajectory design powered by diffusion models. INTRODUCTION Diffusion models are a type of generative model that have achieved state-of-the-art performance across creative and scientific domains. Concerning trajectory design, diffusion models have shown promising results in robotics. Janner et al. propose combining diffusion models with reinforcement learning techniques to develop flexible trajectory planning strategies.

Resistor networks have recently had a surge of interest as substrates for energy-efficient self-learning machines. This work studies the computational capabilities of these resistor networks. We show that electrical networks composed of voltage sources, linear resistors, diodes and voltage-controlled voltage sources (VCVS) can implement any continuous functions. To prove it, we assume that the circuit elements are ideal and that the conductances of variable resistors and the amplification factors of the VCVS's can take arbitrary values -- arbitrarily small or arbitrarily large. The constructive nature of our proof could also inform the design of such self-learning electrical networks.

Concentrated solar power (CSP) is one of the growing technologies that is leading the process of changing from fossil fuels to renewable energies. The sophistication and size of the systems require an increase in maintenance tasks to ensure reliability, availability, maintainability and safety. Currently, automatic fault detection in CSP plants using Parabolic Trough Collector systems evidences two main drawbacks: 1) the devices in use needs to be manually placed near the receiver tube, 2) the Machine Learning-based solutions are not tested in real plants. We address both gaps by combining the data extracted with the use of an Unmaned Aerial Vehicle, and the data provided by sensors placed within 7 real plants. The resulting dataset is the first one of this type and can help to standardize research activities for the problem of fault detection in this type of plants. Our work proposes supervised machine-learning algorithms for detecting broken envelopes of the absorber tubes in CSP plants. The proposed solution takes the class imbalance problem into account, boosting the accuracy of the algorithms for the minority class without harming the overall performance of the models. For a Deep Residual Network, we solve an imbalance and a balance problem at the same time, which increases by 5% the Recall of the minority class with no harm to the F1-score. Additionally, the Random Under Sampling technique boost the performance of traditional Machine Learning models, being the Histogram Gradient Boost Classifier the algorithm with the highest increase (3%) in the F1-Score. To the best of our knowledge, this paper is the first providing an automated solution to this problem using data from operating plants.

This work introduces distributional relational networks (DRNs), a knowledge representation (KR) framework which focuses on allowing semantic approximations over large-scale and heterogeneous knowledge bases. The proposed model uses the distributional semantics information embedded in large text/data corpora to provide a comprehensive and principled solution for semantic approximation. DRNs can be applied to open domain knowledge bases and can be used as a KR model for commonsense reasoning. Experimental results show the suitability of DRNs as a semantically flexible KR framework.

The estimation of unknown values of parameters (or hidden variables, control variables) that characterise a physical system often relies on the comparison of measured data with synthetic data produced by some numerical simulator of the system as the parameter values are varied. This process often encounters two major difficulties: the generation of synthetic data for each considered set of parameter values can be computationally expensive if the system model is complicated; and the exploration of the parameter space can be inefficient and/or incomplete, a typical example being when the exploration becomes trapped in a local optimum of the objection function that characterises the mismatch between the measured and synthetic data. A method to address both these issues is presented, whereby: a surrogate model (or proxy), which emulates the computationally expensive system simulator, is constructed using deep recurrent networks (DRN); and a nested sampling (NS) algorithm is employed to perform efficient and robust exploration of the parameter space. The analysis is performed in a Bayesian context, in which the samples characterise the full joint posterior distribution of the parameters, from which parameter estimates and uncertainties are easily derived. The proposed approach is compared with conventional methods in some numerical examples, for which the results demonstrate that one can accelerate the parameter estimation process by at least an order of magnitude.

While deep neural networks have achieved groundbreaking prediction results in many tasks, there is a class of data where existing architectures are not optimal -- sequences of probability distributions. Performing forward prediction on sequences of distributions has many important applications. However, there are two main challenges in designing a network model for this task. First, neural networks are unable to encode distributions compactly as each node encodes just a real value. A recent work of Distribution Regression Network (DRN) solved this problem with a novel network that encodes an entire distribution in a single node, resulting in improved accuracies while using much fewer parameters than neural networks. However, despite its compact distribution representation, DRN does not address the second challenge, which is the need to model time dependencies in a sequence of distributions. In this paper, we propose our Recurrent Distribution Regression Network (RDRN) which adopts a recurrent architecture for DRN. The combination of compact distribution representation and shared weights architecture across time steps makes RDRN suitable for modeling the time dependencies in a distribution sequence. Compared to neural networks and DRN, RDRN achieves the best prediction performance while keeping the network compact.

We introduce our Distribution Regression Network (DRN) which performs regression from input probability distributions to output probability distributions. Compared to existing methods, DRN learns with fewer model parameters and easily extends to multiple input and multiple output distributions. On synthetic and real-world datasets, DRN performs similarly or better than the state-of-the-art. The field of regression analysis is largely established with methods ranging from linear least squares to multilayer perceptrons. However, the scope of the regression is mostly limited to real valued inputs and outputs (Fiori et al., 2015; Marquardt, 1963). In this paper, we perform distribution-to- distribution regression where one regresses from input probability distributions to output probability distributions. Distribution-to-distribution regression (see work by Oliva et al. (2013)) has not been as widely studied compared to the related task of functional regression (Ferraty & Vieu, 2006). Nevertheless, regression on distributions has many relevant applications. In the study of human populations, probability distributions capture the collective characteristics of the people.