The data drawn from biological, economic, and social systems are often confounded due to the presence of unmeasured variables. Prior work in causal discovery has focused on discrete search procedures for selecting acyclic directed mixed graphs (ADMGs), specifically ancestral ADMGs, that encode ordinary conditional independence constraints among the observed variables of the system. However, confounded systems also exhibit more general equality restrictions that cannot be represented via these graphs, placing a limit on the kinds of structures that can be learned using ancestral ADMGs. In this work, we derive differentiable algebraic constraints that fully characterize the space of ancestral ADMGs, as well as more general classes of ADMGs, arid ADMGs and bow-free ADMGs, that capture all equality restrictions on the observed variables. We use these constraints to cast causal discovery as a continuous optimization problem and design differentiable procedures to find the best fitting ADMG when the data comes from a confounded linear system of equations with correlated errors. We demonstrate the efficacy of our method through simulations and application to a protein expression dataset.

Stochastic kriging has been widely employed for simulation metamodeling to predict the response surface of a complex simulation model. However, its use is limited to cases where the design space is low-dimensional, because the number of design points required for stochastic kriging to produce accurate prediction, in general, grows exponentially in the dimension of the design space. The large sample size results in both a prohibitive sample cost for running the simulation model and a severe computational challenge due to the need of inverting large covariance matrices. Based on tensor Markov kernels and sparse grid experimental designs, we develop a novel methodology that dramatically alleviates the curse of dimensionality. We show that the sample complexity of the proposed methodology grows very mildly in the dimension, even under model misspecification. We also develop fast algorithms that compute stochastic kriging in its exact form without any approximation schemes. We demonstrate via extensive numerical experiments that our methodology can handle problems with a design space of hundreds of dimensions, improving both prediction accuracy and computational efficiency by orders of magnitude relative to typical alternative methods in practice.

The Restricted Boltzmann Machine (RBM) is a stochastic neural network capable of solving a variety of difficult tasks such as NP-Hard combinatorial optimization problems and integer factorization. The RBM architecture is also very compact; requiring very few weights and biases. This, along with its simple, parallelizable sampling algorithm for finding the ground state of such problems, makes the RBM amenable to hardware acceleration. However, training of the RBM on these problems can pose a significant challenge, as the training algorithm tends to fail for large problem sizes and efficient mappings can be hard to find. Here, we propose a method of combining RBMs together that avoids the need to train large problems in their full form. We also propose methods for making the RBM more hardware amenable, allowing the algorithm to be efficiently mapped to an FPGA-based accelerator. Using this accelerator, we are able to show hardware accelerated factorization of 16 bit numbers with high accuracy with a speed improvement of 10000x and a power improvement of 32x.

Augmented-reality (AR) glasses that will have access to onboard sensors and an ability to display relevant information to the user present an opportunity to provide user assistance in quotidian tasks. Many such tasks can be characterized as object-rearrangement tasks. We introduce a novel framework for computing and displaying AR assistance that consists of (1) associating an optimal action sequence with the policy of an embodied agent and (2) presenting this sequence to the user as suggestions in the AR system's heads-up display. The embodied agent comprises a "hybrid" between the AR system and the user, with the AR system's observation space (i.e., sensors) and the user's action space (i.e., task-execution actions); its policy is learned by minimizing the task-completion time. In this initial study, we assume that the AR system's observations include the environment's map and localization of the objects and the user. These choices allow us to formalize the problem of computing AR assistance for any object-rearrangement task as a planning problem, specifically as a capacitated vehicle-routing problem. Further, we introduce a novel AR simulator that can enable web-based evaluation of AR-like assistance and associated at-scale data collection via the Habitat simulator for embodied artificial intelligence. Finally, we perform a study that evaluates user response to the proposed form of AR assistance on a specific quotidian object-rearrangement task, house cleaning, using our proposed AR simulator on mechanical turk. In particular, we study the effect of the proposed AR assistance on users' task performance and sense of agency over a range of task difficulties. Our results indicate that providing users with such assistance improves their overall performance and while users report a negative impact to their agency, they may still prefer the proposed assistance to having no assistance at all.

In this case, GTN will be used in automatic differentiation of weighted finite-state transducers (WFSTs), which is an expressive and powerful graph. This framework enables the separation of graphs from operations on them that helps in exploring new structured loss functions and which in turn makes the encoding of prior knowledge on learning algorithms easier. Further, in a paper published by Awni Hannun, Vineel Pratap, Jacob Kahn & Wei-Ning Hsu of the Facebook AI Research, in this regard, proposed a convolutional WFST layer to be used in the interior of a deep neural network for mapping lower-level to higher-level representations. GTN is written in C and has bindings to Python. GTN can be used to express and design sequence-level loss functions.

Naive Bayes classifiers are a collection of classification algorithms based on Bayes' Theorem. It is not a single algorithm but a family of algorithms where all of them share a common principle, i.e. every pair of features being classified is independent of each other. The dataset is divided into two parts, namely, feature matrix and the response/target vector. Side Note: The assumptions made by Naive Bayes are not generally correct in real-world situations. In-fact, the independence assumption is often not meet and this is why it is called "Naive" i.e. because it assumes something that might not be true.

Hamiltonian Monte Carlo (HMC) is a Markov chain Monte Carlo (MCMC) approach that exhibits favourable exploration properties in high-dimensional models such as neural networks. Unfortunately, HMC has limited use in large-data regimes and little work has explored suitable approaches that aim to preserve the entire Hamiltonian. In our work, we introduce a new symmetric integration scheme for split HMC that does not rely on stochastic gradients. We show that our new formulation is more efficient than previous approaches and is easy to implement with a single GPU. As a result, we are able to perform full HMC over common deep learning architectures using entire data sets. In addition, when we compare with stochastic gradient MCMC, we show that our method achieves better performance in both accuracy and uncertainty quantification. Our approach demonstrates HMC as a feasible option when considering inference schemes for large-scale machine learning problems.

Sparse models are desirable for many applications across diverse domains as they can perform automatic variable selection, aid interpretability, and provide regularization. When fitting sparse models in a Bayesian framework, however, analytically obtaining a posterior distribution over the parameters of interest is intractable for all but the simplest cases. As a result practitioners must rely on either sampling algorithms such as Markov chain Monte Carlo or variational methods to obtain an approximate posterior. Mean field variational inference is a particularly simple and popular framework that is often amenable to analytically deriving closed-form parameter updates. When all distributions in the model are members of exponential families and are conditionally conjugate, optimization schemes can often be derived by hand. Yet, I show that using standard mean field variational inference can fail to produce sensible results for models with sparsity-inducing priors, such as the spike-and-slab. Fortunately, such pathological behavior can be remedied as I show that mixtures of exponential family distributions with non-overlapping support form an exponential family. In particular, any mixture of a diffuse exponential family and a point mass at zero to model sparsity forms an exponential family. Furthermore, specific choices of these distributions maintain conditional conjugacy. I use two applications to motivate these results: one from statistical genetics that has connections to generalized least squares with a spike-and-slab prior on the regression coefficients; and sparse probabilistic principal component analysis. The theoretical results presented here are broadly applicable beyond these two examples.

This work presents a novel posterior inference method for models with intractable evidence and likelihood functions. Error-guided likelihood-free MCMC, or EG-LF-MCMC in short, has been developed for scientific applications, where a researcher is interested in obtaining approximate posterior densities over model parameters, while avoiding the need for expensive training of component estimators on full observational data or the tedious design of expressive summary statistics, as in related approaches. Our technique is based on two phases. In the first phase, we draw samples from the prior, simulate respective observations and record their errors $\epsilon$ in relation to the true observation. We train a classifier to distinguish between corresponding and non-corresponding $(\epsilon, \boldsymbol{\theta})$-tuples. In the second stage the said classifier is conditioned on the smallest recorded $\epsilon$ value from the training set and employed for the calculation of transition probabilities in a Markov Chain Monte Carlo sampling procedure. By conditioning the MCMC on specific $\epsilon$ values, our method may also be used in an amortized fashion to infer posterior densities for observations, which are located a given distance away from the observed data. We evaluate the proposed method on benchmark problems with semantically and structurally different data and compare its performance against the state of the art approximate Bayesian computation (ABC).

Cardio/cerebrovascular diseases (CVD) were the first cause of mortality worldwide in 2015, causing 31% of deaths according to World Health Organization [Organization, 2015]. Blood platelets play a key role in the occurrence of these cardio/cerebrovascular accidents in addition to complex process of blood coagulation, involving adhesion, aggregation and spreading on the vascular wall to stop a hemorrhage while avoiding the vessel occlusion. Although, in a recent biomedical evaluation study by Breet et al. [2010], the correlation between the clinical biological measures using platelet function tests and the occurrence of a cardiovascular event was found to be null for half of the techniques and rather modest for others, indicating the evident need for a more efficient tool or method to monitor patient platelet functionalities. This may be due to the fact that no current test allows the analysis of the different stages of platelet activation or the prediction of the in-vivo behavior of those platelets [Picker, 2011, Koltai et al., 2017]. In addition, the current clinical tests do not take into account the dynamic aspect of the process of platelet aggregation formation and the role that red blood cells can have in this process. To address these issues, Chopard et al. [2017b] provided a physical description of the adhesion and aggregation of platelets in the Impact-R device, by combining digital holography microscopy and mathematical modeling. They have developed a numerical model that quantitatively describes how platelets in a shear flow adhere and aggregate on a deposition surface. Further Dutta et al. [2018] showed how the five parameters of this model, specifying the deposition process and relevant for biomedical understanding of the phenomena, can be inferred from the blood sample collected from an individual using approximate Bayesian computation (ABC) [Lintusaari et al., 2017]. Our main claim here is that the values of some these parameters (eg.