It is important to forecast dam inflow for flood damage mitigation. The hydrograph provides critical information such as the start time, peak level, and volume. Particularly, dam management requires a 6-h lead time of the dam inflow forecast based on a future hydrograph. The authors propose novel target inflow weights to create an ocean feature vector extracted from the analyzed images of the sea surface. We extracted 4,096 elements of the dimension vector in the fc6 layer of the pre-trained VGG16 network. Subsequently, we reduced it to three dimensions of t-SNE. Furthermore, we created the principal component of the sea temperature weights using PCA. We found that these weights contribute to the stability of predictor importance by numerical experiments. As base regression models, we calibrate the least squares with kernel expansion, the quantile random forest minimized out-of bag error, and the support vector regression with a polynomial kernel. When we compute the predictor importance, we visualize the stability of each variable importance introduced by our proposed weights, compared with other results without weights. We apply our method to a dam at Kanto region in Japan and focus on the trained term from 2007 to 2018, with a limited flood term from June to October. We test the accuracy over the 2019 flood term. Finally, we present the applied results and further statistical learning for unknown flood forecast.

Such a generalization leads to important new applications such as estimating statistical discrepancy among multiple random variables like multi-distribution f-divergence, and bias correction via multiple importance sampling. We then develop a general framework from the perspective of Bregman divergence minimization, where each strictly convex multivariate function induces a proper loss for multi-distribution DRE. We show that our framework leads to methods that strictly generalize their counterparts in binary DRE, as well as new methods that show comparable or superior performance on various downstream tasks. It is such a powerful paradigm because computing density ratio focuses on extracting and preserving contrastive information between two distributions, which is crucial in many tasks. Despite the tremendous success of binary DRE, many applications involve more than two probability distributions and developing density ratio estimation methods among multiple distributions has the potential of advancing various applications such as estimating multi-distribution statistical discrepancy measures (Garcia-Garcia & Williamson, 2012), multi-domain transfer learning, bias correction and variance reduction with multiple importance sampling (Elvira et al., 2019), multi-marginal generative modeling (Cao et al., 2019) and multilingual machine translation (Dong et al., 2015; Aharoni et al., 2019).

It is often of interest to estimate regression functions non-parametrically. Penalized regression (PR) is one statistically-effective, well-studied solution to this problem. Unfortunately, in many cases, finding exact solutions to PR problems is computationally intractable. In this manuscript, we propose a mesh-based approximate solution (MBS) for those scenarios. MBS transforms the complicated functional minimization of NPR, to a finite parameter, discrete convex minimization; and allows us to leverage the tools of modern convex optimization. We show applications of MBS in a number of explicit examples (including both uni- and multi-variate regression), and explore how the number of parameters must increase with our sample-size in order for MBS to maintain the rate-optimality of NPR. We also give an efficient algorithm to minimize the MBS objective while effectively leveraging the sparsity inherent in MBS.

Many learning tasks require observing a sequence of images and making a decision. In a transportation problem of designing and planning for shipping boxes between nodes, we show how to treat the network of nodes and the flows between them as images. These images have useful structural information that can be statistically summarized. Using image compression techniques, we reduce an image down to a set of numbers that contain interpretable geographic information that we call geographic signatures. Using geographic signatures, we learn network structure that can be utilized to recommend future network connectivity. We develop a Bayesian reinforcement algorithm that takes advantage of statistically summarized network information as priors and user-decisions to reinforce an agent's probabilistic decision.

Cross-validation is the standard approach for tuning parameter selection in many non-parametric regression problems. However its use is less common in change-point regression, perhaps as its prediction error-based criterion may appear to permit small spurious changes and hence be less well-suited to estimation of the number and location of change-points. We show that in fact the problems of cross-validation with squared error loss are more severe and can lead to systematic under- or over-estimation of the number of change-points, and highly suboptimal estimation of the mean function in simple settings where changes are easily detectable. We propose two simple approaches to remedy these issues, the first involving the use of absolute error rather than squared error loss, and the second involving modifying the holdout sets used. For the latter, we provide conditions that permit consistent estimation of the number of change-points for a general change-point estimation procedure. We show these conditions are satisfied for optimal partitioning using new results on its performance when supplied with the incorrect number of change-points. Numerical experiments show that the absolute error approach in particular is competitive with common change-point methods using classical tuning parameter choices when error distributions are well-specified, but can substantially outperform these in misspecified models. An implementation of our methodology is available in the R package crossvalidationCP on CRAN.

Understanding kinetics and thermodynamics profile of biomolecules is necessary to understand their functional roles which has a major impact in mechanism driven drug discovery. Molecular dynamics simulation has been routinely used to understand conformational dynamics and molecular recognition in biomolecules. Statistical analysis of high-dimensional spatiotemporal data generated from molecular dynamics simulation requires identification of few low-dimensional variables which can describe essential dynamics of a system without significant loss of informations. In physical chemistry, these low-dimensional variables often called collective variables. Collective variables are used to generated reduced representation of free energy surface and calculate transition probabilities between different metastable basins. However the choice of collective variables is not trivial for complex systems. Collective variables ranges from geometric criteria's such as distances, dihedral angles to abstract ones such as weighted linear combinations of multiple geometric variables. Advent of machine learning algorithms led to increasing use of abstract collective variables to represent biomolecular dynamics. In this review, I will highlight several nuances of commonly used collective variables ranging from geometric to abstract ones. Further, I will put forward some cases where machine learning based collective variables were used to describe simple systems which in principle could have been described by geometric ones. Finally, I will put forward my thoughts on artificial general intelligence and how it can be used to discover and predict collective variables from spatiotemporal data generated by molecular dynamics simulations.

The science of causality explains/determines 'cause-effect' relationship between the entities of a system by providing mathematical tools for the purpose. In spite of all the success and widespread applications of machine-learning (ML) algorithms, these algorithms are based on statistical learning alone. Currently, they are nowhere close to 'human-like' intelligence as they fail to answer and learn based on the important "Why?" questions. Hence, researchers are attempting to integrate ML with the science of causality. Among the many causal learning issues encountered by ML, one is that these algorithms are dumb to the temporal order or structure in data. In this work we develop a machine learning pipeline based on a recently proposed 'neurochaos' feature learning technique (ChaosFEX feature extractor), that helps us to learn generalized causal-structure in given time-series data.

We analyze the problem of simultaneous support recovery and estimation of the coefficient vector ($\beta^*$) in a linear model with independent and identically distributed Normal errors. We apply the penalized least square estimator based on non-linear penalties of stochastic gates (STG) [YLNK20] to estimate the coefficients. Considering Gaussian design matrices we show that under reasonable conditions on dimension and sparsity of $\beta^*$ the STG based estimator converges to the true data generating coefficient vector and also detects its support set with high probability. We propose a new projection based algorithm for linear models setup to improve upon the existing STG estimator that was originally designed for general non-linear models. Our new procedure outperforms many classical estimators for support recovery in synthetic data analysis.

Artificial intelligence is being utilized in many domains as of late, and the legal system is no exception. However, as it stands now, the number of well-annotated datasets pertaining to legal documents from the Supreme Court of the United States (SCOTUS) is very limited for public use. Even though the Supreme Court rulings are public domain knowledge, trying to do meaningful work with them becomes a much greater task due to the need to manually gather and process that data from scratch each time. Hence, our goal is to create a high-quality dataset of SCOTUS court cases so that they may be readily used in natural language processing (NLP) research and other data-driven applications. Additionally, recent advances in NLP provide us with the tools to build predictive models that can be used to reveal patterns that influence court decisions. By using advanced NLP algorithms to analyze previous court cases, the trained models are able to predict and classify a court's judgment given the case's facts from the plaintiff and the defendant in textual format; in other words, the model is emulating a human jury by generating a final verdict.

Semantic segmentation plays a fundamental role in a broad variety of computer vision applications, providing key information for the global understanding of an image. Yet, the state-of-the-art models rely on large amount of annotated samples, which are more expensive to obtain than in tasks such as image classification. Since unlabelled data is instead significantly cheaper to obtain, it is not surprising that Unsupervised Domain Adaptation reached a broad success within the semantic segmentation community. This survey is an effort to summarize five years of this incredibly rapidly growing field, which embraces the importance of semantic segmentation itself and a critical need of adapting segmentation models to new environments. We present the most important semantic segmentation methods; we provide a comprehensive survey on domain adaptation techniques for semantic segmentation; we unveil newer trends such as multi-domain learning, domain generalization, test-time adaptation or source-free domain adaptation; we conclude this survey by describing datasets and benchmarks most widely used in semantic segmentation research. We hope that this survey will provide researchers across academia and industry with a comprehensive reference guide and will help them in fostering new research directions in the field.