Paired estimation of change in parameters of interest over a population plays a central role in several application domains including those in the social sciences, epidemiology, medicine and biology. In these domains, the size of the population under study is often very large, however, the number of observations available per individual in the population is very small (\emph{sparse observations}) which makes the problem challenging. Consider the setting with $N$ independent individuals, each with unknown parameters $(p_i, q_i)$ drawn from some unknown distribution on $[0, 1]^2$. We observe $X_i \sim \text{Bin}(t, p_i)$ before an event and $Y_i \sim \text{Bin}(t, q_i)$ after the event. Provided these paired observations, $\{(X_i, Y_i) \}_{i=1}^N$, our goal is to accurately estimate the \emph{distribution of the change in parameters}, $\delta_i := q_i - p_i$, over the population and properties of interest like the \emph{$\ell_1$-magnitude of the change} with sparse observations ($t\ll N$). We provide \emph{information theoretic lower bounds} on the error in estimating the distribution of change and the $\ell_1$-magnitude of change. Furthermore, we show that the following two step procedure achieves the optimal error bounds: first, estimate the full joint distribution of the paired parameters using the maximum likelihood estimator (MLE) and then estimate the distribution of change and the $\ell_1$-magnitude of change using the joint MLE. Notably, and perhaps surprisingly, these error bounds are of the same order as the minimax optimal error bounds for learning the \emph{full} joint distribution itself (in Wasserstein-1 distance); in other words, estimating the magnitude of the change of parameters over the population is, in a minimax sense, as difficult as estimating the full joint distribution itself.

Learning kinetic systems from data is one of the core challenges in many fields. Identifying stable models is essential for the generalization capabilities of data-driven inference. We introduce a computationally efficient framework, called CausalKinetiX, that identifies structure from discrete time, noisy observations, generated from heterogeneous experiments. The algorithm assumes the existence of an underlying, invariant kinetic model, a key criterion for reproducible research. Results on both simulated and real-world examples suggest that learning the structure of kinetic systems benefits from a causal perspective. The identified variables and models allow for a concise description of the dynamics across multiple experimental settings and can be used for prediction in unseen experiments. We observe significant improvements compared to well established approaches focusing solely on predictive performance, especially for out-of-sample generalization.

Our research focuses on studying and developing methods for reducing the dimensionality of large datasets, common in biomedical applications. A major problem when learning information about patients based on genetic sequencing data is that there are often more feature variables (genetic data) than observations (patients). This makes direct supervised learning difficult. One way of reducing the feature space is to use latent Dirichlet allocation in order to group genetic variants in an unsupervised manner. Latent Dirichlet allocation is a common model in natural language processing, which describes a document as a mixture of topics, each with a probability of generating certain words. This can be generalized as a Bayesian tensor decomposition to account for multiple feature variables. While we made some progress improving and modifying these methods, our significant contributions are with hierarchical topic modeling. We developed distinct methods of incorporating hierarchical topic modeling, based on nested Chinese restaurant processes and Pachinko Allocation Machine, into Bayesian tensor decompositions. We apply these models to predict whether or not patients have autism spectrum disorder based on genetic sequencing data. We examine a dataset from National Database for Autism Research consisting of paired siblings -- one with autism, and the other without -- and counts of their genetic variants. Additionally, we linked the genes with their Reactome biological pathways. We combine this information into a tensor of patients, counts of their genetic variants, and the membership of these genes in pathways. Once we decompose this tensor, we use logistic regression on the reduced features in order to predict if patients have autism. We also perform a similar analysis of a dataset of patients with one of four common types of cancer (breast, lung, prostate, and colorectal).

We apply methods from randomized numerical linear algebra (RandNLA) to develop improved algorithms for the analysis of large-scale time series data. We first develop a new fast algorithm to estimate the leverage scores of an autoregressive (AR) model in big data regimes. We show that the accuracy of approximations lies within $(1+\mathcal{O}(\varepsilon))$ of the true leverage scores with high probability. These theoretical results are subsequently exploited to develop an efficient algorithm, called LSAR, for fitting an appropriate AR model to big time series data. Our proposed algorithm is guaranteed, with high probability, to find the maximum likelihood estimates of the parameters of the underlying true AR model and has a worst case running time that significantly improves those of the state-of-the-art alternatives in big data regimes. Empirical results on large-scale synthetic as well as real data highly support the theoretical results and reveal the efficacy of this new approach. To the best of our knowledge, this paper is the first attempt to establish a nexus between RandNLA and big time series data analysis.

Marlyse is a third-year PhD student in the Computer Science and Artificial Intelligence Laboratory at MIT. She received her B.S. in Aeronautics and Astronautics from MIT in 2017. Her current research in the Model-based Embedded and Robotic Systems Group focuses on multi-vehicle online planning, incorporating complex dynamics and constraints. She is also interested in risk-aware planning, fault protection and diagnosis, and adaptive sampling. Outside of the lab, she enjoys playing soccer, dancing, and reading science fiction.

Learning representations of data is an important problem in statistics and machine learning. While the origin of learning representations can be traced back to factor analysis and multidimensional scaling in statistics, it has become a central theme in deep learning with important applications in computer vision and computational neuroscience. In this article, we review recent advances in learning representations from a statistical perspective. In particular, we review the following two themes: (a) unsupervised learning of vector representations and (b) learning of both vector and matrix representations.

Existing works on disentangled representation learning usually lie on a common assumption: all factors in disentangled representations should be independent. This assumption is about the inner property of disentangled representations, while ignoring their relation with external da ta. T o tackle this problem, we propose another assumption to establish an important relation between data and its disentangled representations via mutual information: the mutual information between each factor of disentangled representations and data should be invariant to other factors. W e formulate this assumption into mathematical equations, and theoretically bridge it with independence and conditional independence of factors. Meanwhile, we show that conditional independence is satisfied in encoders of VAEs due to factorized noise in reparameterization. T o highligh t the importance of our proposed assumption, we show in experiments that violating the assumption leads to dramatic decline of disentanglement. Based on this assumption, we further propose to split the deeper layers in encoder to ensure parameters in these layers are not shared for different factors. The proposed encoder, called Split Encoder, can be applied into models that penalize total correlation, and shows significant improvement in unsupervised learning of disentangled representations and reconstructions.

An Adversarial System to attack and an Authorship Attribution System (AAS) to defend itself against the attacks are analyzed. Defending a system against attacks from an adversarial machine learner can be done by randomly switching between models for the system, by detecting and reacting to changes in the distribution of normal inputs, or by using other methods. Adversarial machine learning is used to identify a system that is being used to map system inputs to outputs. Three types of machine learners are using for the model that is being attacked. The machine learners that are used to model the system being attacked are a Radial Basis Function Support Vector Machine, a Linear Support Vector Machine, and a Feedforward Neural Network. The feature masks are evolved using accuracy as the fitness measure. The system defends itself against adversarial machine learning attacks by identifying inputs that do not match the probability distribution of normal inputs. The system also defends itself against adversarial attacks by randomly switching between the feature masks being used to map system inputs to outputs.

Synthetic biology allows us to bioengineer cells to synthesize novel valuable molecules such as renewable biofuels or anticancer drugs. However, traditional synthetic biology approaches involve ad-hoc non systematic engineering practices, which lead to long development times. Here, we present the Automated Recommendation Tool ( ART), a tool that leverages machine learning and probabilistic modeling techniques to guide synthetic biology in a systematic fashion, without the need for a full mechanistic understanding of the biological system. Using sampling-based optimization, ART provides a set of recommended strains to be built in the next engineering cycle, alongside probabilistic predictions of their production levels. We demonstrate the capabilities of ART on simulated and real data sets and discuss possible difficulties in achieving satisfactory predictive power. 2 Introduction Metabolic engineering 1 enables us to bioengineer cells to synthesize novel valuable molecules such as renewable biofuels 2,3 or anticancer drugs.

--This research proposes a new (old) metric for evaluating goodness of fit in topic models, the coefficient of determination, or R 2 . Within the context of topic modeling, R 2 has the same interpretation that it does when used in a broader class of statistical models. Reporting R 2 with topic models addresses two current problems in topic modeling: a lack of standard cross-contextual evaluation metrics for topic modeling and ease of communication with lay audiences. The author proposes that R 2 should be reported as a standard metric when constructing topic models. I NTRODUCTION According to an often-quoted but never cited definition, "the goodness of fit of a statistical model describes how well it fits a set of observations. Measures of goodness of fit typically summarize the discrepancy between observed values and the values expected under the model in question." 1 Goodness of fit measures vary with the goals of those constructing the statistical model. Inferential goals may emphasize in-sample fit while predictive goals may emphasize out-of-sample fit. Prior information may be included in the goodness of fit measure for Bayesian models, or it may not. Goodness of fit measures may include methods to correct for model overfitting. In short, goodness of fit measures the performance of a statistical model against the ground truth of observed data. Fitting the data well is generally a necessary--though not sufficient--condition for trust in a statistical model, whatever its goals. Of course, goodness of fit is only one concern in statistical modeling.