Recent years have witnessed the rapid growth of machine learning in a wide range of fields such as image recognition, text classification, credit scoring prediction, recommendation system, etc. In spite of their great performance in different sectors, researchers still concern about the mechanism under any machine learning (ML) techniques that are inherently black-box and becoming more complex to achieve higher accuracy. Therefore, interpreting machine learning model is currently a mainstream topic in the research community. However, the traditional interpretable machine learning focuses on the association instead of the causality. This paper provides an overview of causal analysis with the fundamental background and key concepts, and then summarizes most recent causal approaches for interpretable machine learning. The evaluation techniques for assessing method quality, and open problems in causal interpretability are also discussed in this paper.

Respiratory symptoms can be a caused by different underlying conditions, and are often caused by viral infections, such as Influenza-like illnesses or other emerging viruses like the Coronavirus. These respiratory viruses, often, have common symptoms, including coughing, high temperature, congested nose, and difficulty breathing. However, early diagnosis of the type of the virus, can be crucial, especially in cases such as the recent COVID-19 pandemic. One of the factors that contributed to the spread of the pandemic, was the late diagnosis or confusing it with regular flu-like symptoms. Science has proved that one of the possible differentiators of the underlying causes of these different respiratory diseases is coughing, which comes in different types and forms. Therefore, a reliable lab-free tool for early and more accurate diagnosis that can differentiate between different respiratory diseases is very much needed. This paper proposes an end-to-end portable system that can record data from patients with symptom, including coughs (voluntary or involuntary) and translate them into health data for diagnosis, and with the aid of machine learning, classify them into different respiratory illnesses, including COVID-19. With the ongoing efforts to stop the spread of the COVID-19 disease everywhere today, and against similar diseases in the future, our proposed low cost and user-friendly solution can play an important part in the early diagnosis.

Type 2 diabetes (T2DM), one of the most prevalent chronic diseases, affects the glucose metabolism of the human body, which decreases the quantity of life and brings a heavy burden on social medical care. Patients with T2DM are more likely to suffer bone fragility fracture as diabetes affects bone mineral density (BMD). However, the discovery of the determinant factors of BMD in a medical way is expensive and time-consuming. In this paper, we propose a novel algorithm, Prior-Knowledge-driven local Causal structure Learning (PKCL), to discover the underlying causal mechanism between BMD and its factors from the clinical data. Since there exist limited data but redundant prior knowledge for medicine, PKCL adequately utilize the prior knowledge to mine the local causal structure for the target relationship. Combining the medical prior knowledge with the discovered causal relationships, PKCL can achieve more reliable results without long-standing medical statistical experiments. Extensive experiments are conducted on a newly provided clinical data set. The experimental study of PKCL on the data is proved to highly corresponding with existing medical knowledge, which demonstrates the superiority and effectiveness of PKCL. To illustrate the importance of prior knowledge, the result of the algorithm without prior knowledge is also investigated.

Adaptive thermodynamic systems -- such as a biological organism attempting to gain survival advantage, an autonomous robot performing a functional task, or a motor protein transporting intracellular nutrients -- can improve their performance by effectively modeling the regularities and stochasticity in their environments. Analogously, but in a purely computational realm, machine learning algorithms seek to estimate models that capture predictable structure and identify irrelevant noise in training data by optimizing performance measures, such as a model's log-likelihood of having generated the data. Is there a sense in which these computational models are physically preferred? For adaptive physical systems we introduce the organizing principle that thermodynamic work is the most relevant performance measure of advantageously modeling an environment. Specifically, a physical agent's model determines how much useful work it can harvest from an environment. We show that when such agents maximize work production they also maximize their environmental model's log-likelihood, establishing an equivalence between thermodynamics and learning. In this way, work maximization appears as an organizing principle that underlies learning in adaptive thermodynamic systems.

High-dimensional generative models have many applications including image compression, multimedia generation, anomaly detection and data completion. State-of-the-art estimators for natural images are autoregressive, decomposing the joint distribution over pixels into a product of conditionals parameterized by a deep neural network, e.g. a convolutional neural network such as the PixelCNN. However, PixelCNNs only model a single decomposition of the joint, and only a single generation order is efficient. For tasks such as image completion, these models are unable to use much of the observed context. To generate data in arbitrary orders, we introduce LMConv: a simple modification to the standard 2D convolution that allows arbitrary masks to be applied to the weights at each location in the image. Using LMConv, we learn an ensemble of distribution estimators that share parameters but differ in generation order, achieving improved performance on whole-image density estimation (2.89 bpd on unconditional CIFAR10), as well as globally coherent image completions. Our code is available at https://ajayjain.github.io/lmconv.

Typically this requires casting the original deterministic physics-based model into a probabilistic framework where inputs or control variables (CVs) are treated as random variables with probability distributions derived from available experimental data, manufacturing constraints, design criteria, expert judgment, and/or other domain knowledge (e.g., see [1]). Running the physics-based model with CVs sampled according to these distributions yields corresponding realizations of the system response as characterized by quantities of interest (QoIs). Analysis of the uncertainty propagation from the CVs to the QoIs informs decision-making, e.g., it informs engineering decisions aimed at improving the quality and reliability of designed products and helps identify potential risks at early stages in the design and manufacturing process. Quantitatively assessing uncertainty propagation presents a fundamental challenge due to the computational cost of the underlying physics-based model. Even for a low number of CVs and QoIs, uncertainty quantification (UQ) for, e.g., accelerating the simulation-aided design of multiscale systems and data-centric engineering tasks more generally ([2]), requires a large number of repeated observations of QoIs to achieve a high degree of confidence in such an analysis. The sampling cost is further exacerbated in real-world applications where distributions on QoIs are typically non-Gaussian, skewed, and/or mutually correlated, and therefore need to be characterized by their full probability density function (PDF) rather than through summary statistics such as mean and variance. The computational cost of nonparametric methods to estimate these densities can become prohibitively high when using a fully-featured physics-based model to compute each sample. One approach to alleviate the computational burden is to derive a cheaper-to-compute surrogate for the physicsbased model's response enabling much faster generation of output data and thus overcoming computational bottlenecks.

Scaling probabilistic models to large realistic problems and datasets is a key challenge in machine learning. Central to this effort is the development of tractable probabilistic models (TPMs): models whose structure guarantees efficient probabilistic inference algorithms. The current landscape of TPMs is fragmented: there exist various kinds of TPMs with different strengths and weaknesses. Two of the most prominent classes of TPMs are determinantal point processes (DPPs) and probabilistic circuits (PCs). This paper provides the first systematic study of their relationship. We propose a unified analysis and shared language for discussing DPPs and PCs. Then we establish theoretical barriers for the unification of these two families, and prove that there are cases where DPPs have no compact representation as a class of PCs. We close with a perspective on the central problem of unifying these tractable models.

We consider the problem of learning a sparse graph under Laplacian constrained Gaussian graphical models. This problem can be formulated as a penalized maximum likelihood estimation of the precision matrix under Laplacian structural constraints. Like in the classical graphical lasso problem, recent works made use of the $\ell_1$-norm regularization with the goal of promoting sparsity in Laplacian structural precision matrix estimation. However, we find that the widely used $\ell_1$-norm is not effective in imposing a sparse solution in this problem. Through empirical evidence, we observe that the number of nonzero graph weights grows with the increase of the regularization parameter. From a theoretical perspective, we prove that a large regularization parameter will surprisingly lead to a fully connected graph. To address this issue, we propose a nonconvex estimation method by solving a sequence of weighted $\ell_1$-norm penalized sub-problems and prove that the statistical error of the proposed estimator matches the minimax lower bound. To solve each sub-problem, we develop a projected gradient descent algorithm that enjoys a linear convergence rate. Numerical experiments involving synthetic and real-world data sets from the recent COVID-19 pandemic and financial stock markets demonstrate the effectiveness of the proposed method. An open source $\mathsf{R}$ package containing the code for all the experiments is available at https://github.com/mirca/sparseGraph.

Connectionist models such as neural networks suffer from catastrophic forgetting. In this work, we study this problem from the perspective of information theory and define forgetting as the increase of description lengths of previous data when they are compressed with a sequentially learned model. In addition, we show that continual learning approaches based on variational posterior approximation and generative replay can be considered as approximations to two prequential coding methods in compression, namely, the Bayesian mixture code and maximum likelihood (ML) plug-in code. We compare these approaches in terms of both compression and forgetting and empirically study the reasons that limit the performance of continual learning methods based on variational posterior approximation. To address these limitations, we propose a new continual learning method that combines ML plug-in and Bayesian mixture codes.

We consider incremental inference problems from aggregate data for collective dynamics. In particular, we address the problem of estimating the aggregate marginals of a Markov chain from noisy aggregate observations in an incremental (online) fashion. We propose a sliding window Sinkhorn belief propagation (SW-SBP) algorithm that utilizes a sliding window filter of the most recent noisy aggregate observations along with encoded information from discarded observations. Our algorithm is built upon the recently proposed multi-marginal optimal transport based SBP algorithm that leverages standard belief propagation and Sinkhorn algorithm to solve inference problems from aggregate data. We demonstrate the performance of our algorithm on applications such as inferring population flow from aggregate observations.