Logistic regression remains one of the most widely used tools in applied statistics, machine learning and data science. Practical datasets often have a substantial number of features $d$ relative to the sample size $n$. In these cases, the logistic regression maximum likelihood estimator (MLE) is biased, and its standard large-sample approximation is poor. In this paper, we develop an improved method for debiasing predictions and estimating frequentist uncertainty for such datasets. We build on recent work characterizing the asymptotic statistical behavior of the MLE in the regime where the aspect ratio $d / n$, instead of the number of features $d$, remains fixed as $n$ grows. In principle, this approximation facilitates bias and uncertainty corrections, but in practice, these corrections require an estimate of the signal strength of the predictors. Our main contribution is SLOE, an estimator of the signal strength with convergence guarantees that reduces the computation time of estimation and inference by orders of magnitude. The bias correction that this facilitates also reduces the variance of the predictions, yielding narrower confidence intervals with higher (valid) coverage of the true underlying probabilities and parameters. We provide an open source package for this method, available at https://github.com/google-research/sloe-logistic.

When linear models are fit to ill-conditioned or confounded narrow-data, TRACE plots are useful in demonstrating and justifying deliberately biased estimation. This makes TRACE diagnostics powerful "visual" displays. If advanced students of regression are trained in interpretation of Trace plots, they could help admininstrators capable of basic statistical thinking avoid misinterpretations of questionable regression coefficient estimates. All five types of ridge TRACE plots for a wide variety of ridge paths can be explored using R-functions. For example, the RXshrink aug.lars() function generates TRACE s for Least-Angle, Lasso and Forward Stagewise methods (Efron, Hastie, Johnstone and Tibshirani 2004; Hastie and

We study an interesting and challenging problem, learning any part of a Bayesian network (BN) structure. In this challenge, it will be computationally inefficient using existing global BN structure learning algorithms to find an entire BN structure to achieve the part of a BN structure in which we are interested. And local BN structure learning algorithms encounter the false edge orientation problem when they are directly used to tackle this challenging problem. In this paper, we first present a new concept of Expand-Backtracking to explain why local BN structure learning methods have the false edge orientation problem, then propose APSL, an efficient and accurate Any Part of BN Structure Learning algorithm. Specifically, APSL divides the V-structures in a Markov blanket (MB) into two types: collider V-structure and non-collider V-structure, then it starts from a node of interest and recursively finds both collider V-structures and non-collider V-structures in the found MBs, until the part of a BN structure in which we are interested are oriented. To improve the efficiency of APSL, we further design the APSL-FS algorithm using Feature Selection, APSL-FS. Using six benchmark BNs, the extensive experiments have validated the efficiency and accuracy of our methods.

Mixtures of Hidden Markov Models (MHMMs) are frequently used for clustering of sequential data. An important aspect of MHMMs, as of any clustering approach, is that they can be interpretable, allowing for novel insights to be gained from the data. However, without a proper way of measuring interpretability, the evaluation of novel contributions is difficult and it becomes practically impossible to devise techniques that directly optimize this property. In this work, an information-theoretic measure (entropy) is proposed for interpretability of MHMMs, and based on that, a novel approach to improve model interpretability is proposed, i.e., an entropy-regularized Expectation Maximization (EM) algorithm. The new approach aims for reducing the entropy of the Markov chains (involving state transition matrices) within an MHMM, i.e., assigning higher weights to common state transitions during clustering. It is argued that this entropy reduction, in general, leads to improved interpretability since the most influential and important state transitions of the clusters can be more easily identified. An empirical investigation shows that it is possible to improve the interpretability of MHMMs, as measured by entropy, without sacrificing (but rather improving) clustering performance and computational costs, as measured by the v-measure and number of EM iterations, respectively.

In recent years, the importance of studying traffic flows and making predictions on alternative mobility (sharing services) has become increasingly important, as accurate and timely information on the travel flow is important for the successful implementation of systems that increase the quality of sharing services. This need has been accentuated by the current health crisis that requires alternative transport mobility such as electric bike and electric scooter sharing. Considering the new approaches in the world of deep learning and the difficulty due to the strong spatial and temporal dependence of this problem, we propose a framework, called STREED-Net, with multi-attention (Spatial and Temporal) able to better mining the high-level spatial and temporal features. We conduct experiments on three real datasets to predict the Inflow and Outflow of the different regions into which the city has been divided. The results indicate that the proposed STREED-Net model improves the state-of-the-art for this problem.

Given two sources of evidence about a latent variable, one can combine the information from both by multiplying the likelihoods of each piece of evidence. However, when one or both of the observation models are misspecified, the distributions will conflict. We study this problem in the setting with two conflicting reward functions learned from different sources. In such a setting, we would like to retreat to a broader distribution over reward functions, in order to mitigate the effects of misspecification. We assume that an agent will maximize expected reward given this distribution over reward functions, and identify four desiderata for this setting. We propose a novel algorithm, Multitask Inverse Reward Design (MIRD), and compare it to a range of simple baselines. While all methods must trade off between conservatism and informativeness, through a combination of theory and empirical results on a toy environment, we find that MIRD and its variant MIRD-IF strike a good balance between the two.

The options framework for hierarchical reinforcement learning has increased its popularity in recent years and has made improvements in tackling the scalability problem in reinforcement learning. Yet, most of these recent successes are linked with a proper options initialization or discovery. When an expert is available, the options discovery problem can be addressed by learning an options-type hierarchical policy directly from expert demonstrations. This problem is referred to as hierarchical imitation learning and can be handled as an inference problem in a Hidden Markov Model, which is done via an Expectation-Maximization type algorithm. In this work, we propose a novel online algorithm to perform hierarchical imitation learning in the options framework. Further, we discuss the benefits of such an algorithm and compare it with its batch version in classical reinforcement learning benchmarks. We show that this approach works well in both discrete and continuous environments and, under certain conditions, it outperforms the batch version.

We develop a novel hybrid method for Bayesian network structure learning called partitioned hybrid greedy search (pHGS), composed of three distinct yet compatible new algorithms: Partitioned PC (pPC) accelerates skeleton learning via a divide-and-conquer strategy, $p$-value adjacency thresholding (PATH) effectively accomplishes parameter tuning with a single execution, and hybrid greedy initialization (HGI) maximally utilizes constraint-based information to obtain a high-scoring and well-performing initial graph for greedy search. We establish structure learning consistency of our algorithms in the large-sample limit, and empirically validate our methods individually and collectively through extensive numerical comparisons. The combined merits of pPC and PATH achieve significant computational reductions compared to the PC algorithm without sacrificing the accuracy of estimated structures, and our generally applicable HGI strategy reliably improves the estimation structural accuracy of popular hybrid algorithms with negligible additional computational expense. Our empirical results demonstrate the superior empirical performance of pHGS against many state-of-the-art structure learning algorithms.

Mapping of spatial hotspots, i.e., regions with significantly higher rates or probability density of generating certain events (e.g., disease or crime cases), is a important task in diverse societal domains, including public health, public safety, transportation, agriculture, environmental science, etc. Clustering techniques required by these domains differ from traditional clustering methods due to the high economic and social costs of spurious results (e.g., false alarms of crime clusters). As a result, statistical rigor is needed explicitly to control the rate of spurious detections. To address this challenge, techniques for statistically-robust clustering have been extensively studied by the data mining and statistics communities. In this survey we present an up-to-date and detailed review of the models and algorithms developed by this field. We first present a general taxonomy of the clustering process with statistical rigor, covering key steps of data and statistical modeling, region enumeration and maximization, significance testing, and data update. We further discuss different paradigms and methods within each of key steps. Finally, we highlight research gaps and potential future directions, which may serve as a stepping stone in generating new ideas and thoughts in this growing field and beyond.

In this paper we perform a numerious numerical studies for the problem of low-rank matrix completion. We compare the Bayesain approaches and a recently introduced de-biased estimator which provides a useful way to build confidence intervals of interest. From a theoretical viewpoint, the de-biased estimator comes with a sharp minimax-optinmal rate of estimation error whereas the Bayesian approach reaches this rate with an additional logarithmic factor. Our simulation studies show originally interesting results that the de-biased estimator is just as good as the Bayesain estimators. Moreover, Bayesian approaches are much more stable and can outperform the de-biased estimator in the case of small samples. However, we also find that the length of the confidence intervals revealed by the de-biased estimator for an entry is absolutely shorter than the length of the considered credible interval. These suggest further theoretical studies on the estimation error and the concentration for Bayesian methods as they are being quite limited up to present.