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.

Advancing probabilistic solar forecasting methods is essential to supporting the integration of solar energy into the electricity grid. In this work, we develop a variety of state-of-the-art probabilistic models for forecasting solar irradiance. We investigate the use of post-hoc calibration techniques for ensuring well-calibrated probabilistic predictions. We train and evaluate the models using public data from seven stations in the SURFRAD network, and demonstrate that the best model, NGBoost, achieves higher performance at an intra-hourly resolution than the best benchmark solar irradiance forecasting model across all stations. Further, we show that NGBoost with CRUDE post-hoc calibration achieves comparable performance to a numerical weather prediction model on hourly-resolution forecasting.

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.

We propose a novel framework for non-parametric policy evaluation in static and dynamic settings. Under the assumption of selection on observables, we consider treatment effects of the population, of sub-populations, and of alternative populations that may have alternative covariate distributions. We further consider the decomposition of a total effect into a direct effect and an indirect effect (as mediated by a particular mechanism). Under the assumption of sequential selection on observables, we consider the effects of sequences of treatments. Across settings, we allow for treatments that may be discrete, continuous, or even text. Across settings, we allow for estimation of not only counterfactual mean outcomes but also counterfactual distributions of outcomes. We unify analyses across settings by showing that all of these causal learning problems reduce to the re-weighting of a prediction, i.e. causal adjustment. We implement the re-weighting as an inner product in a function space called a reproducing kernel Hilbert space (RKHS), with a closed form solution that can be computed in one line of code. We prove uniform consistency and provide finite sample rates of convergence. We evaluate our estimators in simulations devised by other authors. We use our new estimators to evaluate continuous and heterogeneous treatment effects of the US Jobs Corps training program for disadvantaged youth.

Normalizing flows model complex probability distributions by combining a base distribution with a series of bijective neural networks. State-of-the-art architectures rely on coupling and autoregressive transformations to lift up invertible functions from scalars to vectors. In this work, we revisit these transformations as probabilistic graphical models, showing they reduce to Bayesian networks with a pre-defined topology and a learnable density at each node. From this new perspective, we propose the graphical normalizing flow, a new invertible transformation with either a prescribed or a learnable graphical structure. This model provides a promising way to inject domain knowledge into normalizing flows while preserving both the interpretability of Bayesian networks and the representation capacity of normalizing flows. We show that graphical conditioners discover relevant graph structure when we cannot hypothesize it. In addition, we analyze the effect of $\ell_1$-penalization on the recovered structure and on the quality of the resulting density estimation. Finally, we show that graphical conditioners lead to competitive white box density estimators.

A Random Graph is a random object which take its values in the space of graphs. We take advantage of the expressibility of graphs in order to model the uncertainty about the existence of causal relationships within a given set of variables. We adopt a Bayesian point of view in order to capture a causal structure via interaction and learning with a causal environment. We test our method over two different scenarios, and the experiments mainly confirm that our technique can learn a causal structure. Furthermore, the experiments and results presented for the first test scenario demonstrate the usefulness of our method to learn a causal structure as well as the optimal action. On the other hand the second experiment, shows that our proposal manages to learn the underlying causal structure of several tasks with different sizes and different causal structures.