This paper presents a taxonomy of explainability in Human-Agent Systems. We consider fundamental questions about the Why, Who, What, When and How of explainability. First, we define explainability, and its relationship to the related terms of interpretability, transparency, explicitness, and faithfulness. These definitions allow us to answer why explainability is needed in the system, whom it is geared to and what explanations can be generated to meet this need. We then consider when the user should be presented with this information. Last, we consider how objective and subjective measures can be used to evaluate the entire system. This last question is the most encompassing as it will need to evaluate all other issues regarding explainability.

The deep image prior was recently introduced as a prior for natural images. It represents images as the output of a convolutional network with random inputs. For "inference", gradient descent is performed to adjust network parameters to make the output match observations. This approach yields good performance on a range of image reconstruction tasks. We show that the deep image prior is asymptotically equivalent to a stationary Gaussian process prior in the limit as the number of channels in each layer of the network goes to infinity, and derive the corresponding kernel. This informs a Bayesian approach to inference. We show that by conducting posterior inference using stochastic gradient Langevin we avoid the need for early stopping, which is a drawback of the current approach, and improve results for denoising and impainting tasks. We illustrate these intuitions on a number of 1D and 2D signal reconstruction tasks.

Intricating cardiac complexities are the primary factor associated with healthcare costs and the highest cause of death rate in the world. However, preventive measures like the early detection of cardiac anomalies can prevent severe cardiovascular arrests of varying complexities and can impose a substantial impact on healthcare cost. Encountering such scenarios usually the electrocardiogram (ECG or EKG) is the first diagnostic choice of a medical practitioner or clinical staff to measure the electrical and muscular fitness of an individual heart. This paper presents a system which is capable of reading the recorded ECG and predict the cardiac anomalies without the intervention of a human expert. The paper purpose an algorithm which read and perform analysis on electrocardiogram datasets. The proposed architecture uses the Discrete Wavelet Transform (DWT) at first place to perform preprocessing of ECG data followed by undecimated Wavelet transform (UWT) to extract nine relevant features which are of high interest to a cardiologist. The probabilistic mode named Bayesian Network Classifier is trained using the extracted nine parameters on UCL arrhythmia dataset. The proposed system classifies a recorded heartbeat into four classes using Bayesian Network classifier and Tukey's box analysis. The four classes for the prediction of a heartbeat are (a) Normal Beat, (b) Premature Ventricular Contraction (PVC) (c) Premature Atrial Contraction (PAC) and (d) Myocardial Infarction. The results of experimental setup depict that the proposed system has achieved an average accuracy of 96.6 for PAC\% 92.8\% for MI and 87\% for PVC, with an average error rate of 3.3\% for PAC, 6\% for MI and 12.5\% for PVC on real electrocardiogram datasets including Physionet and European ST-T Database (EDB).

Machine learning has made major advances in categorizing objects in images, yet the best algorithms miss important aspects of how people learn and think about categories. People can learn richer concepts from fewer examples, including causal models that explain how members of a category are formed. Here, we explore the limits of this human ability to infer causal "programs" -- latent generating processes with nontrivial algorithmic properties -- from one, two, or three visual examples. People were asked to extrapolate the programs in several ways, for both classifying and generating new examples. As a theory of these inductive abilities, we present a Bayesian program learning model that searches the space of programs for the best explanation of the observations. Although variable, people's judgments are broadly consistent with the model and inconsistent with several alternatives, including a pre-trained deep neural network for object recognition, indicating that people can learn and reason with rich algorithmic abstractions from sparse input data.

This paper considers a new family of variational distributions motivated by Sklar's theorem. This family is based on new copula-like densities on the hypercube with non-uniform marginals which can be sampled efficiently, i.e. with a complexity linear in the dimension of state space. Then, the proposed variational densities that we suggest can be seen as arising from these copula-like densities used as base distributions on the hypercube with Gaussian quantile functions and sparse rotation matrices as normalizing flows. The latter correspond to a rotation of the marginals with complexity $\mathcal{O}(d \log d)$. We provide some empirical evidence that such a variational family can also approximate non-Gaussian posteriors and can be beneficial compared to Gaussian approximations. Our method performs largely comparably to state-of-the-art variational approximations on standard regression and classification benchmarks for Bayesian Neural Networks.

The Cox proportional hazards model is ubiquitous in the analysis of time-to-event data. However, when the data dimension p is comparable to the sample size $N$, maximum likelihood estimates for its regression parameters are known to be biased or break down entirely due to overfitting. This prompted the introduction of the so-called regularized Cox model. In this paper we use the replica method from statistical physics to investigate the relationship between the true and inferred regression parameters in regularized multivariate Cox regression with L2 regularization, in the regime where both p and N are large but with p/N ~ O(1). We thereby generalize a recent study from maximum likelihood to maximum a posteriori inference. We also establish a relationship between the optimal regularization parameter and p/N, allowing for straightforward overfitting corrections in time-to-event analysis.

The standard Gibbs sampler of Mixed Multinomial Logit (MMNL) models involves sampling from conditional densities of utility parameters using Metropolis-Hastings (MH) algorithm due to unavailability of conjugate prior for logit kernel. To address this non-conjugacy concern, we propose the application of P\'olygamma data augmentation (PG-DA) technique for the MMNL estimation. The posterior estimates of the augmented and the default Gibbs sampler are similar for two-alternative scenario (binary choice), but we encounter empirical identification issues in the case of more alternatives ($J \geq 3$).

Spectral embedding of adjacency or Laplacian matrices of undirected graphs is a common technique for representing a network in a lower dimensional latent space, with optimal theoretical guarantees. The embedding can be used to estimate the community structure of the network, with strong consistency results in the stochastic blockmodel framework. One of the main practical limitations of standard algorithms for community detection from spectral embeddings is that the number of communities and the latent dimension of the embedding must be specified in advance. In this article, a novel Bayesian model for simultaneous and automatic selection of the appropriate dimension of the latent space and the number of blocks is proposed. Extensions to directed and bipartite graphs are discussed. The model is tested on simulated and real world network data, showing promising performance for recovering latent community structure.

Given a set of empirical observations, conditional density estimation aims to capture the statistical relationship between a conditional variable $\mathbf{x}$ and a dependent variable $\mathbf{y}$ by modeling their conditional probability $p(\mathbf{y}|\mathbf{x})$. The paper develops best practices for conditional density estimation for finance applications with neural networks, grounded on mathematical insights and empirical evaluations. In particular, we introduce a noise regularization and data normalization scheme, alleviating problems with over-fitting, initialization and hyper-parameter sensitivity of such estimators. We compare our proposed methodology with popular semi- and non-parametric density estimators, underpin its effectiveness in various benchmarks on simulated and Euro Stoxx 50 data and show its superior performance. Our methodology allows to obtain high-quality estimators for statistical expectations of higher moments, quantiles and non-linear return transformations, with very little assumptions about the return dynamic.

In this paper, we consider advancing web-scale knowledge extraction and alignment by integrating OpenIE extractions in the form of (subject, predicate, object) triples with Knowledge Bases (KB). Traditional techniques from universal schema and from schema mapping fall in two extremes: either they perform instance-level inference relying on embedding for (subject, object) pairs, thus cannot handle pairs absent in any existing triples; or they perform predicate-level mapping and completely ignore background evidence from individual entities, thus cannot achieve satisfying quality. We propose OpenKI to handle sparsity of OpenIE extractions by performing instance-level inference: for each entity, we encode the rich information in its neighborhood in both KB and OpenIE extractions, and leverage this information in relation inference by exploring different methods of aggregation and attention. In order to handle unseen entities, our model is designed without creating entity-specific parameters. Extensive experiments show that this method not only significantly improves state-of-the-art for conventional OpenIE extractions like ReVerb, but also boosts the performance on OpenIE from semi-structured data, where new entity pairs are abundant and data are fairly sparse.