Models used for many important engineering and natural systems are imperfect. The discrepancy between the mathematical representations of a true physical system and its imperfect model is called the model error. These model errors can lead to substantial difference between the numerical solutions of the model and the observations of the system, particularly in those involving nonlinear, multi-scale phenomena. Thus, there is substantial interest in reducing model errors, particularly through understanding their physics and sources and leveraging the rapid growth of observational data. Here we introduce a framework named MEDIDA: Model Error Discovery with Interpretability and Data Assimilation. MEDIDA only requires a working numerical solver of the model and a small number of noise-free or noisy sporadic observations of the system. In MEDIDA, first the model error is estimated from differences between the observed states and model-predicted states (the latter are obtained from a number of one-time-step numerical integrations from the previous observed states). If observations are noisy, a data assimilation (DA) technique such as ensemble Kalman filter (EnKF) is first used to provide a noise-free analysis state of the system, which is then used in estimating the model error. Finally, an equation-discovery technique, such as the relevance vector machine (RVM), a sparsity-promoting Bayesian method, is used to identify an interpretable, parsimonious, closed-form representation of the model error. Using the chaotic Kuramoto-Sivashinsky (KS) system as the test case, we demonstrate the excellent performance of MEDIDA in discovering different types of structural/parametric model errors, representing different types of missing physics, using noise-free and noisy observations.

In many areas of science, complex phenomena are modeled by stochastic parametric simulators, often featuring high-dimensional parameter spaces and intractable likelihoods. In this context, performing Bayesian inference can be challenging. In this work, we present a novel method that enables amortized inference over arbitrary subsets of the parameters, without resorting to numerical integration, which makes interpretation of the posterior more convenient. Our method is efficient and can be implemented with arbitrary neural network architectures. We demonstrate the applicability of the method on parameter inference of binary black hole systems from gravitational waves observations.

We present the winning strategy of an electricity demand forecasting competition. This competition was organized to design new forecasting methods for unstable periods such as the one starting in Spring 2020. We rely on state-space models to adapt standard statistical and machine learning models. We claim that it achieves the right compromise between two extremes. On the one hand, purely time-series models such as autoregressives are adaptive in essence but fail to capture dependence to exogenous variables. On the other hand, machine learning methods allow to learn complex dependence to explanatory variables on a historical data set but fail to forecast non-stationary data accurately. The evaluation period of the competition was the occasion of trial and error and we put the focus on the final forecasting procedure. In particular, it was at the same time that a recent algorithm was designed to adapt the variances of a state-space model and we present the results of the final version only. We discuss day-today predictions nonetheless.

An increasingly common use case for machine learning models is augmenting the abilities of human decision makers. For classification tasks where neither the human or model are perfectly accurate, a key step in obtaining high performance is combining their individual predictions in a manner that leverages their relative strengths. In this work, we develop a set of algorithms that combine the probabilistic output of a model with the class-level output of a human. We show theoretically that the accuracy of our combination model is driven not only by the individual human and model accuracies, but also by the model's confidence. Empirical results on image classification with CIFAR-10 and a subset of ImageNet demonstrate that such human-model combinations consistently have higher accuracies than the model or human alone, and that the parameters of the combination method can be estimated effectively with as few as ten labeled datapoints.

Width-based planning has shown promising results on Atari 2600 games using pixel input, while using substantially fewer environment interactions than reinforcement learning. Recent width-based approaches have computed feature vectors for each screen using a hand designed feature set or a variational autoencoder (VAE) trained on game screens, and prune screens that do not have novel features during the search. In this paper, we explore consideration of uncertainty in features generated by a VAE during width-based planning. Our primary contribution is the introduction of active learning to maximize the utility of screens observed during planning. Experimental results demonstrate that use of active learning strategies increases gameplay scores compared to alternative width-based approaches with equal numbers of environment interactions.

In this work, we propose a Deep neural network-assisted Particle Filter-based (DePF) approach to address the Mobile User (MU) joint synchronization and localization (sync\&loc) problem in ultra dense networks. In particular, DePF deploys an asymmetric time-stamp exchange mechanism between the MUs and the Access Points (APs), which, traditionally, provides us with information about the MUs' clock offset and skew. However, information about the distance between an AP and an MU is also intrinsic to the propagation delay experienced by exchanged time-stamps. In addition, to estimate the angle of arrival of the received synchronization packet, DePF draws on the multiple signal classification algorithm that is fed by Channel Impulse Response (CIR) experienced by the sync packets. The CIR is also leveraged on to determine the link condition, i.e. Line-of-Sight (LoS) or Non-LoS. Finally, to perform joint sync\&loc, DePF capitalizes on particle Gaussian mixtures that allow for a hybrid particle-based and parametric Bayesian Recursive Filtering (BRF) fusion of the aforementioned pieces of information and thus jointly estimate the position and clock parameters of the MUs. The simulation results verifies the superiority of the proposed algorithm over the state-of-the-art schemes, especially that of Extended Kalman filter- and linearized BRF-based joint sync\&loc. In particular, only drawing on the synchronization time-stamp exchange and CIRs, for 90$\%$of the cases, the absolute position and clock offset estimation error remain below 1 meter and 2 nanoseconds, respectively.

Scientific discovery concerns finding patterns in data and creating insightful hypotheses that explain these patterns. Traditionally, this process required human ingenuity, but with the galloping advances in artificial intelligence (AI) it becomes feasible to automate some parts of scientific discovery. In this work we leverage AI for strategy discovery for understanding human planning. In the state-of-the-art methods data about the process of human planning is often used to group similar behaviors together and formulate verbal descriptions of the strategies which might underlie those groups. Here, we automate these two steps. Our algorithm, called Human-Interpret, uses imitation learning to describe process-tracing data collected in psychological experiments with the Mouselab-MDP paradigm in terms of a procedural formula. Then, it translates that formula to natural language using a pre-defined predicate dictionary. We test our method on a benchmark data set that researchers have previously scrutinized manually. We find that the descriptions of human planning strategies obtained automatically are about as understandable as human-generated descriptions. They also cover a substantial proportion of all types of human planning strategies that had been discovered manually. Our method saves scientists' time and effort as all the reasoning about human planning is done automatically. This might make it feasible to more rapidly scale up the search for yet undiscovered cognitive strategies to many new decision environments, populations, tasks, and domains. Given these results, we believe that the presented work may accelerate scientific discovery in psychology, and due to its generality, extend to problems from other fields.

We derive a novel information-theoretic analysis of the generalization property of meta-learning algorithms. Concretely, our analysis proposes a generic understanding of both the conventional learning-to-learn framework and the modern model-agnostic meta-learning (MAML) algorithms. Moreover, we provide a data-dependent generalization bound for a stochastic variant of MAML, which is non-vacuous for deep few-shot learning. As compared to previous bounds that depend on the square norm of gradients, empirical validations on both simulated data and a well-known few-shot benchmark show that our bound is orders of magnitude tighter in most situations.

Voice conversion is a common speech synthesis task which can be solved in different ways depending on a particular real-world scenario. The most challenging one often referred to as one-shot many-to-many voice conversion consists in copying the target voice from only one reference utterance in the most general case when both source and target speakers do not belong to the training dataset. We present a scalable high-quality solution based on diffusion probabilistic modeling and demonstrate its superior quality compared to state-of-the-art one-shot voice conversion approaches. Moreover, focusing on real-time applications, we investigate general principles which can make diffusion models faster while keeping synthesis quality at a high level. As a result, we develop a novel Stochastic Differential Equations solver suitable for various diffusion model types and generative tasks as shown through empirical studies and justify it by theoretical analysis.

Parametric Bayesian Inference: Implementation of Numerical Sampling Techniques with Proofs. Acceptance/Rejection Sampling & MCMC Metropolis-Hastings Sampling with full Computational Simulation.