In the area of credit risk analytics, current Bankruptcy Prediction Models (BPMs) struggle with (a) the availability of comprehensive and real-world data sets and (b) the presence of extreme class imbalance in the data (i.e., very few samples for the minority class) that degrades the performance of the prediction model. Moreover, little research has compared the relative performance of well-known BPM's on public datasets addressing the class imbalance problem. In this work, we apply eight classes of well-known BPMs, as suggested by a review of decades of literature, on a new public dataset named Freddie Mac Single-Family Loan-Level Dataset with resampling (i.e., adding synthetic minority samples) of the minority class to tackle class imbalance. Additionally, we apply some recent AI techniques (e.g., tree-based ensemble techniques) that demonstrate potentially better results on models trained with resampled data. In addition, from the analysis of 19 years (1999-2017) of data, we discover that models behave differently when presented with sudden changes in the economy (e.g., a global financial crisis) resulting in abrupt fluctuations in the national default rate. In summary, this study should aid practitioners/researchers in determining the appropriate model with respect to data that contains a class imbalance and various economic stages.

--Discovering human mobility patterns with geo-location data collected from smartphone users has been a hot research topic in recent years. In this paper, we attempt to discover daily mobile patterns based on GPS data. We view this problem from a probabilistic perspective in order to explore more information from the original GPS data compared to other conventional methods. A non-parameter Bayesian modeling method, Infinite Gaussian Mixture Model, is used to estimate the probability density for the daily mobility. Then, we use Kullback-Leibler divergence as the metrics to measure the similarity of different probability distributions. And combining Infinite Gaussian Mixture Model and Kullback-Leibler divergence, we derived an automatic clustering algorithm to discover mobility patterns for each individual user without setting the number of clusters in advance. In the experiments, the effectiveness of our method is validated on the real user data collected from different users. The results show that the IGMM-based algorithm outperforms the GMM-based algorithm. We also test our methods on the dataset with different lengths to discover the minimum data length for discovering mobility patterns. I NTRODUCTION S MARTPHONEdevices are equipped with multiple sensors that can record user behavior on the handsets. With the help of a large-scale smartphone usage data, researchers are able to study human behavior in the real world.

Bayesian neural networks (BNNs) introduce uncertainty estimation to deep networks by performing Bayesian inference on network weights. However, such models bring the challenges of inference, and further BNNs with weight uncertainty rarely achieve superior performance to standard models. In this paper, we investigate a new line of Bayesian deep learning by performing Bayesian reasoning on the structure of deep neural networks. Drawing inspiration from the neural architecture search, we define the network structure as gating weights on the redundant operations between computational nodes, and apply stochastic variational inference techniques to learn the structure distributions of networks. Empirically, the proposed method substantially surpasses the advanced deep neural networks across a range of classification and segmentation tasks. More importantly, our approach also preserves benefits of Bayesian principles, producing improved uncertainty estimation than the strong baselines including MC dropout and variational BNNs algorithms (e.g. noisy EK-FAC).

Gibbs sampling is a Markov chain Monte Carlo method that is often used for learning and inference on graphical models. Minibatching, in which a small random subset of the graph is used at each iteration, can help make Gibbs sampling scale to large graphical models by reducing its computational cost. In this paper, we propose a new auxiliary-variable minibatched Gibbs sampling method, {\it Poisson-minibatching Gibbs}, which both produces unbiased samples and has a theoretical guarantee on its convergence rate. In comparison to previous minibatched Gibbs algorithms, Poisson-minibatching Gibbs supports fast sampling from continuous state spaces and avoids the need for a Metropolis-Hastings correction on discrete state spaces. We demonstrate the effectiveness of our method on multiple applications and in comparison with both plain Gibbs and previous minibatched methods.

Markov chain Monte Carlo (MCMC) algorithm, a generic sampling method, is ubiquitous in modern statistics, especially in Bayesian fields. MCMC algorithms require only the evaluation of the target pointwise, up to a multiple constant, in order to sample from it. In Bayesian analysis, the object of main interest is the posterior, which is not in closed form in general, and MCMC has become a standard tool in this domain. However, MCMC is difficult to scale and its applications are limited when the observation size is very large, for it needs to sweep over the entire observations set in order to evaluate the likelihood function at each iteration. Recently, many methods have been proposed to better scale MCMC algorithms for big data sets and these can be roughly classified into two groups Bardenet et al. (2017): divide-and-conquer methods and subsampling-based methods. For divide-and-conquer methods, one splits the whole data set into subsets, runs MCMC over each subset to generate samples of parameters and combine these to produce an approximation of the true posterior. Depending on how MCMC is handled over the subsets, these methods can be further classified into two sub-categories.

Information theory provides a mathematical foundation to measure uncertainty in belief. Belief is represented by a probability distribution that captures our understanding of an outcome's plausibility. Information measures based on Shannon's concept of entropy include realization information, Kullback-Leibler divergence, Lindley's information in experiment, cross entropy, and mutual information. We derive a general theory of information from first principles that accounts for evolving belief and recovers all of these measures. Rather than simply gauging uncertainty, information is understood in this theory to measure change in belief. We may then regard entropy as the information we expect to gain upon realization of a discrete latent random variable. This theory of information is compatible with the Bayesian paradigm in which rational belief is updated as evidence becomes available. Furthermore, this theory admits novel measures of information with well-defined properties, which we explore in both analysis and experiment. This view of information illuminates the study of machine learning by allowing us to quantify information captured by a predictive model and distinguish it from residual information contained in training data. We gain related insights regarding feature selection, anomaly detection, and novel Bayesian approaches.

We consider the problem of identifying universal low-dimensional features from high-dimensional data for inference tasks in settings involving learning. For such problems, we introduce natural notions of universality and we show a local equivalence among them. Our analysis is naturally expressed via information geometry, and represents a conceptually and computationally useful analysis. The development reveals the complementary roles of the singular value decomposition, Hirschfeld-Gebelein-R\'enyi maximal correlation, the canonical correlation and principle component analyses of Hotelling and Pearson, Tishby's information bottleneck, Wyner's common information, Ky Fan $k$-norms, and Brieman and Friedman's alternating conditional expectations algorithm. We further illustrate how this framework facilitates understanding and optimizing aspects of learning systems, including multinomial logistic (softmax) regression and the associated neural network architecture, matrix factorization methods for collaborative filtering and other applications, rank-constrained multivariate linear regression, and forms of semi-supervised learning.

Often the development of novel materials is not amenable to high-throughput or purely computational screening methods. Instead, materials must be synthesized one at a time in a process that does not generate significant amounts of data. One way this method can be improved is by ensuring that each experiment provides the best improvement in both material properties and predictive modeling accuracy. In this work, we study the effectiveness of active learning, which optimizes the order of experiments, and meta learning, which transfers knowledge from one context to another, to reduce the number of experiments necessary to build a predictive model. We present a novel multi-task benchmark database of peptides designed to advance active, few-shot, and meta-learning methods for experimental design. Each task is binary classification of peptides represented as a sequence string. We show results of standard active learning and meta-learning methods across these datasets to assess their ability to improve predictive models with the fewest number of experiments. We find the ensemble query by committee active learning method to be effective. The meta-learning method Reptile was found to improve accuracy. The robustness of these conclusions were tested across multiple model choices.

Due to limited computational power, performing uncertainty quantification analyses with complex computational models can be a challenging task. This is exacerbated in the context of stochastic simulators, the response of which to a given set of input parameters, rather than being a deterministic value, is a random variable with unknown probability density function (PDF). Of interest in this paper is the construction of a surrogate that can accurately predict this response PDF for any input parameters. We suggest using a flexible distribution family -- the generalized lambda distribution -- to approximate the response PDF. The associated distribution parameters are cast as functions of input parameters and represented by sparse polynomial chaos expansions. To build such a surrogate model, we propose an approach based on a local inference of the response PDF at each point of the experimental design based on replicated model evaluations. Two versions of this framework are proposed and compared on analytical examples and case studies.

It is a particularly well-suited approach to better understand the underlying structure of data when scientific understanding of the data is at an early stage. BN modelling is designed to sort out directly from indirectly related variables and offers a far richer modelling framework than classical approaches in epidemiology like, e.g., regression techniques or extensions thereof. In contrast to structural equation modelling (Hair, Black, Babin, Anderson, Tatham et al. 1998), which requires expert knowledge to design the model, the Additive Bayesian Network (ABN) method is a data-driven approach (Lewis and Ward 2013; Kratzer, Pittavino, Lewis, and Furrer 2019b). It does not rely on expert knowledge, but it can possiarXiv:1911.09006v1