Current modeling approaches for hydrological modeling often rely on either physics-based or data-science methods, including Machine Learning (ML) algorithms. While physics-based models tend to rigid structure resulting in unrealistic parameter values in certain instances, ML algorithms establish the input-output relationship while ignoring the constraints imposed by well-known physical processes. While there is a notion that the physics model enables better process understanding and ML algorithms exhibit better predictive skills, scientific knowledge that does not add to predictive ability may be deceptive. Hence, there is a need for a hybrid modeling approach to couple ML algorithms and physics-based models in a synergistic manner. Here we develop a Physics Informed Machine Learning (PIML) model that combines the process understanding of conceptual hydrological model with predictive abilities of state-of-the-art ML models. We apply the proposed model to predict the monthly time series of the target (streamflow) and intermediate variables (actual evapotranspiration) in the Narmada river basin in India. Our results show the capability of the PIML model to outperform a purely conceptual model ($abcd$ model) and ML algorithms while ensuring the physical consistency in outputs validated through water balance analysis. The systematic approach for combining conceptual model structure with ML algorithms could be used to improve the predictive accuracy of crucial hydrological processes important for flood risk assessment.

In machine learning and data science, we often consider efficiency for solving problems. In sparse estimation, such as fused lasso and convex clustering, we apply either the proximal gradient method or the alternating direction method of multipliers (ADMM) to solve the problem. It takes time to include matrix division in the former case, while an efficient method such as FISTA (fast iterative shrinkage-thresholding algorithm) has been developed in the latter case. This paper proposes a general method for converting the ADMM solution to the proximal gradient method, assuming that the constraints and objectives are strongly convex. Then, we apply it to sparse estimation problems, such as sparse convex clustering and trend filtering, and we show by numerical experiments that we can obtain a significant improvement in terms of efficiency.

UMAP has supplanted t-SNE as state-of-the-art for visualizing high-dimensional datasets in many disciplines, but the reason for its success is not well understood. In this work, we investigate UMAP's sampling based optimization scheme in detail. We derive UMAP's effective loss function in closed form and find that it differs from the published one. As a consequence, we show that UMAP does not aim to reproduce its theoretically motivated high-dimensional UMAP similarities. Instead, it tries to reproduce similarities that only encode the shared $k$ nearest neighbor graph, thereby challenging the previous understanding of UMAP's effectiveness. Instead, we claim that the key to UMAP's success is its implicit balancing of attraction and repulsion resulting from negative sampling. This balancing in turn facilitates optimization via gradient descent. We corroborate our theoretical findings on toy and single cell RNA sequencing data.

This article describes a novel approach to expand in run-time the knowledge base of an Artificial Conversational Agent. A technique for automatic knowledge extraction from the user's sentence and four methods to insert the new acquired concepts in the knowledge base have been developed and integrated into a system that has already been tested for knowledge-based conversation between a social humanoid robot and residents of care homes. The run-time addition of new knowledge allows overcoming some limitations that affect most robots and chatbots: the incapability of engaging the user for a long time due to the restricted number of conversation topics. The insertion in the knowledge base of new concepts recognized in the user's sentence is expected to result in a wider range of topics that can be covered during an interaction, making the conversation less repetitive. Two experiments are presented to assess the performance of the knowledge extraction technique, and the efficiency of the developed insertion methods when adding several concepts in the Ontology.

In this paper we examine, how the dynamic laws governing the time evolution of a time series can be identified. We give a finite difference equation as well as a differential equation representation for that. We also study, how the required symmetries, like time reversal can be imposed on the laws. We study the compression performance of linear laws on sound data.

Recently the vision transformer (ViT) architecture, where the backbone purely consists of self-attention mechanism, has achieved very promising performance in visual classification. However, the high performance of the original ViT heavily depends on pretraining using ultra large-scale datasets, and it significantly underperforms on ImageNet-1K if trained from scratch. This paper makes the efforts toward addressing this problem, by carefully considering the role of visual tokens. First, for classification head, existing ViT only exploits class token while entirely neglecting rich semantic information inherent in high-level visual tokens. Therefore, we propose a new classification paradigm, where the second-order, cross-covariance pooling of visual tokens is combined with class token for final classification. Meanwhile, a fast singular value power normalization is proposed for improving the second-order pooling. Second, the original ViT employs the naive embedding of fixed-size image patches, lacking the ability to model translation equivariance and locality. To alleviate this problem, we develop a light-weight, hierarchical module based on off-the-shelf convolutions for visual token embedding. The proposed architecture, which we call So-ViT, is thoroughly evaluated on ImageNet-1K. The results show our models, when trained from scratch, outperform the competing ViT variants, while being on par with or better than state-of-the-art CNN models. Code is available at https://github.com/jiangtaoxie/So-ViT

Click-Through Rate (CTR) prediction is a core task in nowadays commercial recommender systems. Feature crossing, as the mainline of research on CTR prediction, has shown a promising way to enhance predictive performance. Even though various models are able to learn feature interactions without manual feature engineering, they rarely attempt to individually learn representations for different feature structures. In particular, they mainly focus on the modeling of cross sparse features but neglect to specifically represent cross dense features. Motivated by this, we propose a novel Extreme Cross Network, abbreviated XCrossNet, which aims at learning dense and sparse feature interactions in an explicit manner. XCrossNet as a feature structure-oriented model leads to a more expressive representation and a more precise CTR prediction, which is not only explicit and interpretable, but also time-efficient and easy to implement.

"Machine intelligence is the last invention that humanity will ever need to make". The quote definitely makes it clear that machine learning is the future and vast opportunities and benefits for all. Let this be a fresh start for you to learn a really interesting algorithm in machine learning. As you all know, we often come across the problems of storing and processing huge data in machine learning tasks, as it's a time-consuming process and difficulties to interpret also arises. Not every feature of the data is necessary for predictions.

Motivation: The activity of the adaptive immune system is governed by T-cells and their specific T-cell receptors (TCR), which selectively recognize foreign antigens. Recent advances in experimental techniques have enabled sequencing of TCRs and their antigenic targets (epitopes), allowing to research the missing link between TCR sequence and epitope binding specificity. Scarcity of data and a large sequence space make this task challenging, and to date only models limited to a small set of epitopes have achieved good performance. Here, we establish a k-nearest-neighbor (K-NN) classifier as a strong baseline and then propose TITAN (Tcr epITope bimodal Attention Networks), a bimodal neural network that explicitly encodes both TCR sequences and epitopes to enable the independent study of generalization capabilities to unseen TCRs and/or epitopes. Results: By encoding epitopes at the atomic level with SMILES sequences, we leverage transfer learning and data augmentation to enrich the input data space and boost performance. TITAN achieves high performance in the prediction of specificity of unseen TCRs (ROC-AUC 0.87 in 10-fold CV) and surpasses the results of the current state-of-the-art (ImRex) by a large margin. Notably, our Levenshtein-distance-based K-NN classifier also exhibits competitive performance on unseen TCRs. While the generalization to unseen epitopes remains challenging, we report two major breakthroughs. First, by dissecting the attention heatmaps, we demonstrate that the sparsity of available epitope data favors an implicit treatment of epitopes as classes. This may be a general problem that limits unseen epitope performance for sufficiently complex models. Second, we show that TITAN nevertheless exhibits significantly improved performance on unseen epitopes and is capable of focusing attention on chemically meaningful molecular structures.

Finding communities in networks is a problem that remains difficult, in spite of the amount of attention it has recently received. The Stochastic Block-Model (SBM) is a generative model for graphs with "communities" for which, because of its simplicity, the theoretical understanding has advanced fast in recent years. In particular, there have been various results showing that simple versions of spectral clustering using the Normalized Laplacian of the graph can recover the communities almost perfectly with high probability. Here we show that essentially the same algorithm used for the SBM and for its extension called Degree-Corrected SBM, works on a wider class of Block-Models, which we call Preference Frame Models, with essentially the same guarantees. Moreover, the parametrization we introduce clearly exhibits the free parameters needed to specify this class of models, and results in bounds that expose with more clarity the parameters that control the recovery error in this model class.