Abstract--Bayesian networks are powerful statistical models to study the probabilistic relationships among set random variables with major applications in disease modeling and prediction. Here, we propose a continuous time Bayesian network with conditional dependencies, represented as Poisson regression, to model the impact of exogenous variables on the conditional dependencies of the network. We also propose an adaptive regularization method with an intuitive early stopping feature based on density based clustering for efficient learning of the structure and parameters of the proposed network. Using a dataset of patients with multiple chronic conditions extracted from electronic health records of the Department of Veterans Affairs we compare the performance of the proposed approach with some of the existing methods in the literature for both short-term (one-year ahead) and long-term (multi-year ahead) predictions. The proposed approach provides a sparse intuitive representation of the complex functional relationships between multiple chronic conditions. It also provides the capability of analyzing multiple disease trajectories over time given any combination of prior conditions.

In this post, I summarize a series of resources to get started with Bayesian Statistics. I compiled these references based on my experience and opinion as to what a good introduction and next steps are in this process. This is not an academic curriculum or anything tremendously rigorous, but it is a comprehensive list that will surely get you embarked on the journey to revisiting/starting your statistics. Many of the references below were recommended to me in several workshops I've attended, and I want to share with those like me that want to be better at statistics and Machine Learning (ML). The first resource I can think of out there for beginners interested in Bayesian statistics and modeling is Richard McElreath's Statistical Rethinking.

Solutions to most complex tasks can be decomposed into simpler, intermediate skills, reusable across wider ranges of problems. We follow this concept and introduce Hindsight Off-policy Options (HO2), a new algorithm for efficient and robust option learning. The algorithm relies on critic-weighted maximum likelihood estimation and an efficient dynamic programming inference procedure over off-policy trajectories. We can backpropagate through the inference procedure through time and the policy components for every time-step, making it possible to train all component's parameters off-policy, independently of the data-generating behavior policy. Experimentally, we demonstrate that HO2 outperforms competitive baselines and solves demanding robot stacking and ball-in-cup tasks from raw pixel inputs in simulation. We further compare autoregressive option policies with simple mixture policies, providing insights into the relative impact of two types of abstractions common in the options framework: action abstraction and temporal abstraction. Finally, we illustrate challenges caused by stale data in off-policy options learning and provide effective solutions.

Recent advances in neural network-based generative modeling have reignited the hopes in having computer systems capable of seamlessly conversing with humans and able to understand natural language. Neural architectures have been employed to generate text excerpts to various degrees of success, in a multitude of contexts and tasks that fulfil various user needs. Notably, high capacity deep learning models trained on large scale datasets demonstrate unparalleled abilities to learn patterns in the data even in the lack of explicit supervision signals, opening up a plethora of new possibilities regarding producing realistic and coherent texts. While the field of natural language generation is evolving rapidly, there are still many open challenges to address. In this survey we formally define and categorize the problem of natural language generation. We review particular application tasks that are instantiations of these general formulations, in which generating natural language is of practical importance. Next we include a comprehensive outline of methods and neural architectures employed for generating diverse texts. Nevertheless, there is no standard way to assess the quality of text produced by these generative models, which constitutes a serious bottleneck towards the progress of the field. To this end, we also review current approaches to evaluating natural language generation systems. We hope this survey will provide an informative overview of formulations, methods, and assessments of neural natural language generation.

The exogeneity bias and instrument validation have always been critical topics in statistics, machine learning and biostatistics. In the era of big data, such issues typically come with dimensionality issue and, hence, require even more attention than ever. In this paper we ensemble two well-known tools from machine learning and biostatistics -- stable variable selection and random graph -- and apply them to estimating the house pricing mechanics and the follow-up socio-economic effect on the 2010 Sydney house data. The estimation is conducted on an over-200-gigabyte ultrahigh dimensional database consisting of local education data, GIS information, census data, house transaction and other socio-economic records. The technique ensemble carefully improves the variable selection sparisty, stability and robustness to high dimensionality, complicated causal structures and the consequent multicollinearity, which is ultimately helpful on the data-driven recovery of a sparse and intuitive causal structure. The new ensemble also reveals its efficiency and effectiveness on endogeneity detection, instrument validation, weak instruments pruning and selection of proper instruments. From the perspective of machine learning, the estimation result both aligns with and confirms the facts of Sydney house market, the classical economic theories and the previous findings of simultaneous equations modeling. Moreover, the estimation result is totally consistent with and supported by the classical econometric tool like two-stage least square regression and different instrument tests (the code can be found at https://github.com/isaac2math/solar_graph_learning).

In this paper we focus on the variable-selection peformance of solar on the empirical data with complicated dependence structures and, hence, severe multicollinearity and grouping effect issues. We choose the prostate cancer data and the Sydney house price data and apply two lasso solvers, elastic net and solar on them (code can be found at \url{https://github.com/isaac2math/}). The results shows that (i) lasso is affected by the grouping effect and randomly drop variables with high correlations, resulting unreliable and uninterpretable results; (ii) elastic net is more robust to grouping effect; however, it completely lose variable-selection sparsity when the dependence structure of the data is complicated; (iii) solar demonstrates its superior robustness to complicated dependence structures and grouping effect, returning variable-selection results with better stability and sparsity. Also, such stability and sparsity make solar a reliable variable pre-estimation filter of a linear dependence structure esimation (linear probablistic graph learning). The linear probablistic graph estimated on the variable selected by solar returns an intuitive, sparse and stable dependence structure.

Systems that are based on recursive Bayesian updates for classification limit the cost of evidence collection through certain stopping/termination criteria and accordingly enforce decision making. Conventionally, two termination criteria based on pre-defined thresholds over (i) the maximum of the state posterior distribution; and (ii) the state posterior uncertainty are commonly used. In this paper, we propose a geometric interpretation over the state posterior progression and accordingly we provide a point-by-point analysis over the disadvantages of using such conventional termination criteria. For example, through the proposed geometric interpretation we show that confidence thresholds defined over maximum of the state posteriors suffer from stiffness that results in unnecessary evidence collection whereas uncertainty based thresholding methods are fragile to number of categories and terminate prematurely if some state candidates are already discovered to be unfavorable. Moreover, both types of termination methods neglect the evolution of posterior updates. We then propose a new stopping/termination criterion with a geometrical insight to overcome the limitations of these conventional methods and provide a comparison in terms of decision accuracy and speed. We validate our claims using simulations and using real experimental data obtained through a brain computer interfaced typing system.

We introduce a class of acquisition functions for sample selection that leads to faster convergence in applications related to Bayesian experimental design and uncertainty quantification. The approach follows the paradigm of active learning, whereby existing samples of a black-box function are utilized to optimize the next most informative sample. The proposed method aims to take advantage of the fact that some input directions of the black-box function have a larger impact on the output than others, which is important especially for systems exhibiting rare and extreme events. The acquisition functions introduced in this work leverage the properties of the likelihood ratio, a quantity that acts as a probabilistic sampling weight and guides the active-learning algorithm towards regions of the input space that are deemed most relevant. We demonstrate superiority of the proposed approach in the uncertainty quantification of a hydrological system as well as the probabilistic quantification of rare events in dynamical systems and the identification of their precursors.

Data quality is a significant issue for any application that requests for analytics to support decision making. It becomes very important when we focus on Internet of Things (IoT) where numerous devices can interact to exchange and process data. IoT devices are connected to Edge Computing (EC) nodes to report the collected data, thus, we have to secure data quality not only at the IoT but also at the edge of the network. In this paper, we focus on the specific problem and propose the use of interpretable machine learning to deliver the features that are important to be based for any data processing activity. Our aim is to secure data quality, at least, for those features that are detected as significant in the collected datasets. We have to notice that the selected features depict the highest correlation with the remaining in every dataset, thus, they can be adopted for dimensionality reduction. We focus on multiple methodologies for having interpretability in our learning models and adopt an ensemble scheme for the final decision. Our scheme is capable of timely retrieving the final result and efficiently select the appropriate features. We evaluate our model through extensive simulations and present numerical results. Our aim is to reveal its performance under various experimental scenarios that we create varying a set of parameters adopted in our mechanism.

We introduce a new incremental preference elicitation procedure able to deal with noisy responses of a Decision Maker (DM). The originality of the contribution is to propose a Bayesian approach for determining a preferred solution in a multiobjective decision problem involving a combinatorial set of alternatives. We assume that the preferences of the DM are represented by an aggregation function whose parameters are unknown and that the uncertainty about them is represented by a density function on the parameter space. Pairwise comparison queries are used to reduce this uncertainty (by Bayesian revision). The query selection strategy is based on the solution of a mixed integer linear program with a combinatorial set of variables and constraints, which requires to use columns and constraints generation methods. Numerical tests are provided to show the practicability of the approach.