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.

This paper describes the NEMO submission to SIGTYP 2020 shared task which deals with prediction of linguistic typological features for multiple languages using the data derived from World Atlas of Language Structures (WALS). We employ frequentist inference to represent correlations between typological features and use this representation to train simple multi-class estimators that predict individual features. We describe two submitted ridge regression-based configurations which ranked second and third overall in the constrained task. Our best configuration achieved the micro-averaged accuracy score of 0.66 on 149 test languages.

Finite Mixture Regression (FMR) refers to the mixture modeling scheme which learns multiple regression models from the training data set. Each of them is in charge of a subset. FMR is an effective scheme for handling sample heterogeneity, where a single regression model is not enough for capturing the complexities of the conditional distribution of the observed samples given the features. In this paper, we propose an FMR model that 1) finds sample clusters and jointly models multiple incomplete mixed-type targets simultaneously, 2) achieves shared feature selection among tasks and cluster components, and 3) detects anomaly tasks or clustered structure among tasks, and accommodates outlier samples. We provide non-asymptotic oracle performance bounds for our model under a high-dimensional learning framework. The proposed model is evaluated on both synthetic and real-world data sets. The results show that our model can achieve state-of-the-art performance.

We consider the parameter estimation problem of a probabilistic generative model prescribed using a natural exponential family of distributions. For this problem, the typical maximum likelihood estimator usually overfits under limited training sample size, is sensitive to noise and may perform poorly on downstream predictive tasks. To mitigate these issues, we propose a distributionally robust maximum likelihood estimator that minimizes the worst-case expected log-loss uniformly over a parametric Kullback-Leibler ball around a parametric nominal distribution. Leveraging the analytical expression of the Kullback-Leibler divergence between two distributions in the same natural exponential family, we show that the min-max estimation problem is tractable in a broad setting, including the robust training of generalized linear models. Our novel robust estimator also enjoys statistical consistency and delivers promising empirical results in both regression and classification tasks.

Federated learning is typically approached as an optimization problem, where the goal is to minimize a global loss function by distributing computation across client devices that possess local data and specify different parts of the global objective. We present an alternative perspective and formulate federated learning as a posterior inference problem, where the goal is to infer a global posterior distribution by having client devices each infer the posterior of their local data. While exact inference is often intractable, this perspective provides a principled way to search for global optima in federated settings. Further, starting with the analysis of federated quadratic objectives, we develop a computation- and communication-efficient approximate posterior inference algorithm -- federated posterior averaging (FedPA). Our algorithm uses MCMC for approximate inference of local posteriors on the clients and efficiently communicates their statistics to the server, where the latter uses them to refine a global estimate of the posterior mode. Finally, we show that FedPA generalizes federated averaging (FedAvg), can similarly benefit from adaptive optimizers, and yields state-of-the-art results on four realistic and challenging benchmarks, converging faster, to better optima.

Prediction is critical for decision-making under uncertainty and lends validity to statistical inference. With targeted prediction, the goal is to optimize predictions for specific decision tasks of interest, which we represent via functionals. Although classical decision analysis extracts predictions from a Bayesian model, these predictions are often difficult to interpret and slow to compute. Instead, we design a class of parametrized actions for Bayesian decision analysis that produce optimal, scalable, and simple targeted predictions. For a wide variety of action parametrizations and loss functions--including linear actions with sparsity constraints for targeted variable selection--we derive a convenient representation of the optimal targeted prediction that yields efficient and interpretable solutions. Customized out-of-sample predictive metrics are developed to evaluate and compare among targeted predictors. Through careful use of the posterior predictive distribution, we introduce a procedure that identifies a set of near-optimal, or acceptable targeted predictors, which provide unique insights into the features and level of complexity needed for accurate targeted prediction. Simulations demonstrate excellent prediction, estimation, and variable selection capabilities. Targeted predictions are constructed for physical activity data from the National Health and Nutrition Examination Survey (NHANES) to better predict and understand the characteristics of intraday physical activity.

Animals are equipped with a rich innate repertoire of sensory, behavioral and motor skills, which allows them to interact with the world immediately after birth. At the same time, many behaviors are highly adaptive and can be tailored to specific environments by means of learning. In this work, we use mathematical analysis and the framework of meta-learning (or'learning to learn') to answer when it is beneficial to learn such an adaptive strategy and when to hard-code a heuristic behavior. We find that the interplay of ecological uncertainty, task complexity and the agents' lifetime has crucial effects on the meta-learned amortized Bayesian inference performed by an agent. There exist two regimes: One in which metalearning yields a learning algorithm that implements task-dependent informationintegration and a second regime in which meta-learning imprints a heuristic or'hard-coded' behavior. Further analysis reveals that nonadaptive behaviors are not only optimal for aspects of the environment that are stable across individuals, but also in situations where an adaptation to the environment would in fact be highly beneficial, but could not be done quickly enough to be exploited within the remaining lifetime. Hard-coded behaviors should hence not only be those that always work, but also those that are too complex to be learned within a reasonable time frame. The'nature versus nurture' debate (e.g., Mutti et al., 1996; Tabery, 2014) - the question which aspects of behavior are'hard-coded' by evolution, and which are learned from experience - is one of the oldest and most controversial debates in biology.