In the standard data analysis framework, data is first collected (once for all), and then data analysis is carried out. With the advancement of digital technology, decisionmakers constantly analyze past data and generate new data through the decisions they make. In this paper, we model this as a Markov decision process and show that the dynamic interaction between data generation and data analysis leads to a new type of bias -- reinforcement bias -- that exacerbates the endogeneity problem in standard data analysis. We propose a class of instrument variable (IV)-based reinforcement learning (RL) algorithms to correct for the bias and establish their asymptotic properties by incorporating them into a two-timescale stochastic approximation framework. A key contribution of the paper is the development of new techniques that allow for the analysis of the algorithms in general settings where noises feature time-dependency. We use the techniques to derive sharper results on finite-time trajectory stability bounds: with a polynomial rate, the entire future trajectory of the iterates from the algorithm fall within a ball that is centered at the true parameter and is shrinking at a (different) polynomial rate. We also use the technique to provide formulas for inferences that are rarely done for RL algorithms. These formulas highlight how the strength of the IV and the degree of the noise's time dependency affect the inference.

As machine learning systems become more powerful they also become increasingly unpredictable and opaque. Yet, finding human-understandable explanations of how they work is essential for their safe deployment. This technical report illustrates a methodology for investigating the causal mechanisms that drive the behaviour of artificial agents. Six use cases are covered, each addressing a typical question an analyst might ask about an agent. In particular, we show that each question cannot be addressed by pure observation alone, but instead requires conducting experiments with systematically chosen manipulations so as to generate the correct causal evidence.

In order to model risk aversion in reinforcement learning, an emerging line of research adapts familiar algorithms to optimize coherent risk functionals, a class that includes conditional value-at-risk (CVaR). Because optimizing the coherent risk is difficult in Markov decision processes, recent work tends to focus on the Markov coherent risk (MCR), a time-consistent surrogate. While, policy gradient (PG) updates have been derived for this objective, it remains unclear (i) whether PG finds a global optimum for MCR; (ii) how to estimate the gradient in a tractable manner. In this paper, we demonstrate that, in general, MCR objectives (unlike the expected return) are not gradient dominated and that stationary points are not, in general, guaranteed to be globally optimal. Moreover, we present a tight upper bound on the suboptimality of the learned policy, characterizing its dependence on the nonlinearity of the objective and the degree of risk aversion. Addressing (ii), we propose a practical implementation of PG that uses state distribution reweighting to overcome previous limitations. Through experiments, we demonstrate that when the optimality gap is small, PG can learn risk-sensitive policies. However, we find that instances with large suboptimality gaps are abundant and easy to construct, outlining an important challenge for future research.

The no free lunch theorem states that no model is better suited to every problem. A question that arises from this is how to design methods that propose optimizers tailored to specific problems achieving state-of-the-art performance. This paper addresses this issue by proposing the use of meta-learning to infer population-based black-box optimizers that can automatically adapt to specific classes of problems. We suggest a general modeling of population-based algorithms that result in Learning-to-Optimize POMDP (LTO-POMDP), a meta-learning framework based on a specific partially observable Markov decision process (POMDP). From that framework's formulation, we propose to parameterize the algorithm using deep recurrent neural networks and use a meta-loss function based on stochastic algorithms' performance to train efficient data-driven optimizers over several related optimization tasks. The learned optimizers' performance based on this implementation is assessed on various black-box optimization tasks and hyperparameter tuning of machine learning models. Our results revealed that the meta-loss function encourages a learned algorithm to alter its search behavior so that it can easily fit into a new context. Thus, it allows better generalization and higher sample efficiency than state-of-the-art generic optimization algorithms, such as the Covariance matrix adaptation evolution strategy (CMA-ES).

This paper presents a machine learning framework (GP-NODE) for Bayesian systems identification from partial, noisy and irregular observations of nonlinear dynamical systems. The proposed method takes advantage of recent developments in differentiable programming to propagate gradient information through ordinary differential equation solvers and perform Bayesian inference with respect to unknown model parameters using Hamiltonian Monte Carlo sampling and Gaussian Process priors over the observed system states. This allows us to exploit temporal correlations in the observed data, and efficiently infer posterior distributions over plausible models with quantified uncertainty. Moreover, the use of sparsity-promoting priors such as the Finnish Horseshoe for free model parameters enables the discovery of interpretable and parsimonious representations for the underlying latent dynamics. A series of numerical studies is presented to demonstrate the effectiveness of the proposed GP-NODE method including predator-prey systems, systems biology, and a 50-dimensional human motion dynamical system. Taken together, our findings put forth a novel, flexible and robust workflow for data-driven model discovery under uncertainty. All code and data accompanying this manuscript are available online at \url{https://github.com/PredictiveIntelligenceLab/GP-NODEs}.

Gaussian processes (GPs) are frequently used in machine learning and statistics to construct powerful models. In a Bayesian setting, GPs provide a probabilistic approach to model unknown functions; specifically, the GP prior assumes that the function evaluated at any finite set of inputs has a Gaussian distribution with consistent parameters, specified by the mean function and symmetric positive definite covariance (or kernel) function. The flexible, probabilistic and nonparametric nature of GP models makes them appropriate and useful in a wide range of applications, including geostatistics [Matheron, 1973], atmospheric sciences [Berrocal et al., 2010], biology [Stathopoulos et al., 2014], inverse problems [Kaipio and Somersalo, 2006], and more. However, when employing GPs in practice, important considerations must be made, specifically, to address the computational burden, approximation of the posterior, form of the covariance function and inference of its hyperparmeters. First, GPs suffer from a high computational burden, due to the need to store and invert large and dense covariance matrices.

It is important for a broad range of applications, including policy making [136], medical imaging [30], advertisement [22], the development of medical treatments [189], the evaluation of evidence within legal frameworks [183, 218], social science [82, 96, 246], biology [235], and many others. It is also a burgeoning topic in machine learning and artificial intelligence [17, 66, 76, 144, 210, 247, 255], where it has been argued that a consideration for causality is crucial for reasoning about the world. In order to discover causal relations, and thereby gain causal understanding, one may perform interventions and manipulations as part of a randomized experiment. These experiments may not only allow researchers or agents to identify causal relationships, but also to estimate the magnitude of these relationships. Unfortunately, in many cases, it may not be possible to undertake such experiments due to prohibitive cost, ethical concerns, or impracticality.

Two popular types of machine translation (MT) are phrase-based and neural machine translation systems. Both of these types of systems are composed of multiple complex models or layers. Each of these models and layers learns different linguistic aspects of the source language. However, for some of these models and layers, it is not clear which linguistic phenomena are learned or how this information is learned. For phrase-based MT systems, it is often clear what information is learned by each model, and the question is rather how this information is learned, especially for its phrase reordering model. For neural machine translation systems, the situation is even more complex, since for many cases it is not exactly clear what information is learned and how it is learned. To shed light on what linguistic phenomena are captured by MT systems, we analyze the behavior of important models in both phrase-based and neural MT systems. We consider phrase reordering models from phrase-based MT systems to investigate which words from inside of a phrase have the biggest impact on defining the phrase reordering behavior. Additionally, to contribute to the interpretability of neural MT systems we study the behavior of the attention model, which is a key component in neural MT systems and the closest model in functionality to phrase reordering models in phrase-based systems. The attention model together with the encoder hidden state representations form the main components to encode source side linguistic information in neural MT. To this end, we also analyze the information captured in the encoder hidden state representations of a neural MT system. We investigate the extent to which syntactic and lexical-semantic information from the source side is captured by hidden state representations of different neural MT architectures.

In the last post on Hidden Markov models (HMM), we never solved the problem of finding the most probable sequence of coins used. If you didn't read the post on HMMs, I would highly encourage you to do so. For those of you who did not, I'll outline the problem. Let's say some guru came up to you and told you to pick a coin from a bag (there are only two coins in the bag) and flip the coin. You'll either observe a head or a tail.

Machine learning has achieved tremendous success in a variety of domains in recent years. However, a lot of these success stories have been in places where the training and the testing distributions are extremely similar to each other. In everyday situations when models are tested in slightly different data than they were trained on, ML algorithms can fail spectacularly. This research attempts to formally define this problem, what sets of assumptions are reasonable to make in our data and what kind of guarantees we hope to obtain from them. Then, we focus on a certain class of out of distribution problems, their assumptions, and introduce simple algorithms that follow from these assumptions that are able to provide more reliable generalization. A central topic in the thesis is the strong link between discovering the causal structure of the data, finding features that are reliable (when using them to predict) regardless of their context, and out of distribution generalization.