Deep neural networks have become an extremely popular learning technique, with significant deployment in a wide variety of practical domains such as computer vision [1, 2, 3], biosignal processing [4, 5], image captioning [6] and speech recognition [7]. With the significant increase in dataset scale and subsequent increase in model complexity of multilayered neural network architectures, it has become imperative to learn networks that can offer performance guarantees, yield good generalization, and provide sparse representations. Vapnik's seminal work in computational learning theory [8] highlighted that a small VC dimension and good generalization go hand in hand, however, minimizing the VC dimension as a function of the weights of the class of networks has remained elusive. The representational redundancy in deep neural networks is well recognized. Some works on model complexity have recently appeared in literature [9, 10]. In many cases, the number of parameters exceeds the amount of training data resulting in severe overfitting [11]. Sontag [12] derived that the VC dimension of neural network with |W | weights is O(|W |log(|W |)), where |W | is the cardinality of total number of weights. Hence, it is essential to reduce the redundancy in weights and neurons and enforce sparsity in the structure to bring down the VC dimension [13, 14]. A number of methods have been proposed in the neural network domain to reduce model complexity [15, 16, 17], but these largely focus on pruning trained networks by removing synapses or neurons through heuristics or by applying sparsity inducing norms (e.g., L

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.

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}.

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.

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.

Labeling data for modern machine learning is expensive and time-consuming. Latent variable models can be used to infer labels from weaker, easier-to-acquire sources operating on unlabeled data. Such models can also be trained using labeled data, presenting a key question: should a user invest in few labeled or many unlabeled points? We answer this via a framework centered on model misspecification in method-of-moments latent variable estimation. Our core result is a bias-variance decomposition of the generalization error, which shows that the unlabeled-only approach incurs additional bias under misspecification. We then introduce a correction that provably removes this bias in certain cases. We apply our decomposition framework to three scenarios -- well-specified, misspecified, and corrected models -- to 1) choose between labeled and unlabeled data and 2) learn from their combination. We observe theoretically and with synthetic experiments that for well-specified models, labeled points are worth a constant factor more than unlabeled points. With misspecification, however, their relative value is higher due to the additional bias but can be reduced with correction. We also apply our approach to study real-world weak supervision techniques for dataset construction.

Missing values exist in nearly all clinical studies because data for a variable or question are not collected or not available. Inadequate handling of missing values can lead to biased results and loss of statistical power in analysis. Existing models usually do not consider privacy concerns or do not utilise the inherent correlations across multiple features to impute the missing values. In healthcare applications, we are usually confronted with high dimensional and sometimes small sample size datasets that need more effective augmentation or imputation techniques. Besides, imputation and augmentation processes are traditionally conducted individually. However, imputing missing values and augmenting data can significantly improve generalisation and avoid bias in machine learning models. A Bayesian approach to impute missing values and creating augmented samples in high dimensional healthcare data is proposed in this work. We propose folded Hamiltonian Monte Carlo (F-HMC) with Bayesian inference as a more practical approach to process the cross-dimensional relations by applying a random walk and Hamiltonian dynamics to adapt posterior distribution and generate large-scale samples. The proposed method is applied to a cancer symptom assessment dataset and confirmed to enrich the quality of data in precision, accuracy, recall, F1 score, and propensity metric.

We develop operators for construction of proposals in probabilistic programs, which we refer to as inference combinators. Inference combinators define a grammar over importance samplers that compose primitive operations such as application of a transition kernel and importance resampling. Proposals in these samplers can be parameterized using neural networks, which in turn can be trained by optimizing variational objectives. The result is a framework for user-programmable variational methods that are correct by construction and can be tailored to specific models. We demonstrate the flexibility of this framework by implementing advanced variational methods based on amortized Gibbs sampling and annealing.

We introduce Deep Adaptive Design (DAD), a general method for amortizing the cost of performing sequential adaptive experiments using the framework of Bayesian optimal experimental design (BOED). Traditional sequential BOED approaches require substantial computational time at each stage of the experiment. This makes them unsuitable for most real-world applications, where decisions must typically be made quickly. DAD addresses this restriction by learning an amortized design network upfront and then using this to rapidly run (multiple) adaptive experiments at deployment time. This network takes as input the data from previous steps, and outputs the next design using a single forward pass; these design decisions can be made in milliseconds during the live experiment. To train the network, we introduce contrastive information bounds that are suitable objectives for the sequential setting, and propose a customized network architecture that exploits key symmetries. We demonstrate that DAD successfully amortizes the process of experimental design, outperforming alternative strategies on a number of problems.