In this article, we'll discuss Gaussian Process Regression (GPR) from first principles, using mathematical concepts from machine learning, optimization, and Bayesian inference. We'll start with Gaussian Processes, use this to formalize how predictions are made with GPR models, and then discuss two crucial ingredients for GPR models: covariance functions and hyperparameter optimization. Finally, we'll build on our mathematical derivations below by discussing some intuitive ways to view GPR. If you'd also like to see these ideas presented as an academic-style paper, please check out this link here. Before we talk about GPR, let's first explore what a Gaussian Process is.

We present RAWLSNET, a system for altering Bayesian Network (BN) models to satisfy the Rawlsian principle of fair equality of opportunity (FEO). RAWLSNET's BN models generate aspirational data distributions: data generated to reflect an ideally fair, FEO-satisfying society. FEO states that everyone with the same talent and willingness to use it should have the same chance of achieving advantageous social positions (e.g., employment), regardless of their background circumstances (e.g., socioeconomic status). Satisfying FEO requires alterations to social structures such as school assignments. Our paper describes RAWLSNET, a method which takes as input a BN representation of an FEO application and alters the BN's parameters so as to satisfy FEO when possible, and minimize deviation from FEO otherwise. We also offer guidance for applying RAWLSNET, including on recognizing proper applications of FEO. We demonstrate the use of our system with publicly available data sets. RAWLSNET's altered BNs offer the novel capability of generating aspirational data for FEO-relevant tasks. Aspirational data are free from the biases of real-world data, and thus are useful for recognizing and detecting sources of unfairness in machine learning algorithms besides biased data.

In this paper it is shown that $C_\beta$-smooth functions can be approximated by neural networks with parameters $\{0,\pm \frac{1}{2}, \pm 1, 2\}$. The depth, width and the number of active parameters of constructed networks have, up to a logarithimc factor, the same dependence on the approximation error as the networks with parameters in $[-1,1]$. In particular, this means that the nonparametric regression estimation with constructed networks attain the same convergence rate as with the sparse networks with parameters in $[-1,1]$.

Policy makers typically face the problem of wanting to estimate the long-term effects of novel treatments, while only having historical data of older treatment options. We assume access to a long-term dataset where only past treatments were administered and a short-term dataset where novel treatments have been administered. We propose a surrogate based approach where we assume that the long-term effect is channeled through a multitude of available short-term proxies. Our work combines three major recent techniques in the causal machine learning literature: surrogate indices, dynamic treatment effect estimation and double machine learning, in a unified pipeline. We show that our method is consistent and provides root-n asymptotically normal estimates under a Markovian assumption on the data and the observational policy. We use a data-set from a major corporation that includes customer investments over a three year period to create a semi-synthetic data distribution where the major qualitative properties of the real dataset are preserved. We evaluate the performance of our method and discuss practical challenges of deploying our formal methodology and how to address them.

In the estimation of the causal effect under linear Structural Causal Models (SCMs), it is common practice to first identify the causal structure, estimate the probability distributions, and then calculate the causal effect. However, if the goal is to estimate the causal effect, it is not necessary to fix a single causal structure or probability distributions. In this paper, we first show from a Bayesian perspective that it is Bayes optimal to weight (average) the causal effects estimated under each model rather than estimating the causal effect under a fixed single model. This idea is also known as Bayesian model averaging. Although the Bayesian model averaging is optimal, as the number of candidate models increases, the weighting calculations become computationally hard. We develop an approximation to the Bayes optimal estimator by using Gaussian scale mixture distributions.

As transparency becomes key for robotics and AI, it will be necessary to evaluate the methods through which transparency is provided, including automatically generated natural language (NL) explanations. Here, we explore parallels between the generation of such explanations and the much-studied field of evaluation of Natural Language Generation (NLG). Specifically, we investigate which of the NLG evaluation measures map well to explanations. We present the ExBAN corpus: a crowd-sourced corpus of NL explanations for Bayesian Networks. We run correlations comparing human subjective ratings with NLG automatic measures. We find that embedding-based automatic NLG evaluation methods, such as BERTScore and BLEURT, have a higher correlation with human ratings, compared to word-overlap metrics, such as BLEU and ROUGE. This work has implications for Explainable AI and transparent robotic and autonomous systems.

Diabetes is currently one of the most common, dangerous, and costly diseases in the world that is caused by an increase in blood sugar or a decrease in insulin in the body. Diabetes can have detrimental effects on people's health if diagnosed late. Today, diabetes has become one of the challenges for health and government officials. Prevention is a priority, and taking care of people's health without compromising their comfort is an essential need. In this study, the Ensemble training methodology based on genetic algorithms are used to accurately diagnose and predict the outcomes of diabetes mellitus. In this study, we use the experimental data, real data on Indian diabetics on the University of California website. Current developments in ICT, such as the Internet of Things, machine learning, and data mining, allow us to provide health strategies with more intelligent capabilities to accurately predict the outcomes of the disease in daily life and the hospital and prevent the progression of this disease and it's many complications. The results show the high performance of the proposed method in diagnosing the disease, which has reached 98.8%, and 99% accuracy in this study.

Building a humanlike integrative artificial cognitive system, that is, an artificial general intelligence, is one of the goals in artificial intelligence and developmental robotics. Furthermore, a computational model that enables an artificial cognitive system to achieve cognitive development will be an excellent reference for brain and cognitive science. This paper describes the development of a cognitive architecture using probabilistic generative models (PGMs) to fully mirror the human cognitive system. The integrative model is called a whole-brain PGM (WB-PGM). It is both brain-inspired and PGMbased. In this paper, the process of building the WB-PGM and learning from the human brain to build cognitive architectures is described.

Diagnosis of chronic diseases and assistance in medical decisions is based on machine learning algorithms. In this paper, we review the classification algorithms used in the health care system (chronic diseases) and present the neural network-based Ensemble learning method. We briefly describe the commonly used algorithms and describe their critical properties. Materials and Methods: In this study, modern classification algorithms used in healthcare, examine the principles of these methods and guidelines, and to accurately diagnose and predict chronic diseases, superior machine learning algorithms with the neural network-based ensemble learning Is used. To do this, we use experimental data, real data on chronic patients (diabetes, heart, cancer) available on the UCI site. Results: We found that group algorithms designed to diagnose chronic diseases can be more effective than baseline algorithms. It also identifies several challenges to further advancing the classification of machine learning in the diagnosis of chronic diseases. Conclusion: The results show the high performance of the neural network-based Ensemble learning approach for the diagnosis and prediction of chronic diseases, which in this study reached 98.5, 99, and 100% accuracy, respectively.

Motivated by the rising abundance of observational data with continuous treatments, we investigate the problem of estimating the average dose-response curve (ADRF). Available parametric methods are limited in their model space, and previous attempts in leveraging neural network to enhance model expressiveness relied on partitioning continuous treatment into blocks and using separate heads for each block; this however produces in practice discontinuous ADRFs. Therefore, the question of how to adapt the structure and training of neural network to estimate ADRFs remains open. This paper makes two important contributions. First, we propose a novel varying coefficient neural network (VCNet) that improves model expressiveness while preserving continuity of the estimated ADRF. Second, to improve finite sample performance, we generalize targeted regularization to obtain a doubly robust estimator of the whole ADRF curve. Continuous treatments arise in many fields, including healthcare, public policy, and economics. With the widespread accumulation of observational data, estimating the average dose-response function (ADRF) while correcting for confounders has become an important problem (Hirano & Imbens, 2004; Imai & Van Dyk, 2004; Kennedy et al., 2017; Fong et al., 2018). Recently, papers in causal inference (Johansson et al., 2016; Alaa & van der Schaar, 2017; Shalit et al., 2017; Schwab et al., 2019; Farrell et al., 2018; Shi et al., 2019) have utilized feed forward neural network for modeling.