Distributionally robust optimization has been shown to offer a principled way to regularize learning models. In this paper, we find that Tikhonov regularization is distributionally robust in an optimal transport sense (i.e., if an adversary chooses distributions in a suitable optimal transport neighborhood of the empirical measure), provided that suitable martingale constraints are also imposed. Further, we introduce a relaxation of the martingale constraints which not only provides a unified viewpoint to a class of existing robust methods but also leads to new regularization tools. To realize these novel tools, tractable computational algorithms are proposed. As a byproduct, the strong duality theorem proved in this paper can be potentially applied to other problems of independent interest.

Arrival/Travel times for public transit exhibit variability on account of factors like seasonality, dwell times at bus stops, traffic signals, travel demand fluctuation etc. The developing world in particular is plagued by additional factors like lack of lane discipline, excess vehicles, diverse modes of transport and so on. This renders the bus arrival time prediction (BATP) to be a challenging problem especially in the developing world. A novel data-driven model based on recurrent neural networks (RNNs) is proposed for BATP (in real-time) in the current work. The model intelligently incorporates both spatial and temporal correlations in a unique (non-linear) fashion distinct from existing approaches. In particular, we propose a Gated Recurrent Unit (GRU) based Encoder-Decoder(ED) OR Seq2Seq RNN model (originally introduced for language translation) for BATP. The geometry of the dynamic real time BATP problem enables a nice fit with the Encoder-Decoder based RNN structure. We feed relevant additional synchronized inputs (from previous trips) at each step of the decoder (a feature classically unexplored in machine translation applications). Further motivated from accurately modelling congestion influences on travel time prediction, we additionally propose to use a bidirectional layer at the decoder (something unexplored in other time-series based ED application contexts). The effectiveness of the proposed algorithms is demonstrated on real field data collected from challenging traffic conditions. Our experiments indicate that the proposed method outperforms diverse existing state-of-art data-driven approaches proposed for the same problem.

We introduce DocSCAN, a completely unsupervised text classification approach using Semantic Clustering by Adopting Nearest-Neighbors (SCAN). For each document, we obtain semantically informative vectors from a large pre-trained language model. Similar documents have proximate vectors, so neighbors in the representation space tend to share topic labels. Our learnable clustering approach uses pairs of neighboring datapoints as a weak learning signal. The proposed approach learns to assign classes to the whole dataset without provided ground-truth labels. On five topic classification benchmarks, we improve on various unsupervised baselines by a large margin. In datasets with relatively few and balanced outcome classes, DocSCAN approaches the performance of supervised classification. The method fails for other types of classification, such as sentiment analysis, pointing to important conceptual and practical differences between classifying images and texts.

Support Vector Machines (SVMs) are one of the most popular supervised learning models to classify using a hyperplane in an Euclidean space. Similar to SVMs, tropical SVMs classify data points using a tropical hyperplane under the tropical metric with the max-plus algebra. In this paper, first we show generalization error bounds of tropical SVMs over the tropical projective torus. While the generalization error bounds attained via Vapnik-Chervonenkis (VC) dimensions in a distribution-free manner still depend on the dimension, we also show numerically and theoretically by extreme value statistics that the tropical SVMs for classifying data points from two Gaussian distributions as well as empirical data sets of different neuron types are fairly robust against the curse of dimensionality. Extreme value statistics also underlie the anomalous scaling behaviors of the tropical distance between random vectors with additional noise dimensions. Finally, we define tropical SVMs over a function space with the tropical metric.

Knowledge graph embedding aims to predict the missing relations between entities in knowledge graphs. Tensor-decomposition-based models, such as ComplEx, provide a good trade-off between efficiency and expressiveness, that is crucial because of the large size of real world knowledge graphs. The recent multi-partition embedding interaction (MEI) model subsumes these models by using the block term tensor format and provides a systematic solution for the trade-off. However, MEI has several drawbacks, some of which carried from its subsumed tensor-decomposition-based models. In this paper, we address these drawbacks and introduce the Multi-partition Embedding Interaction iMproved beyond block term format (MEIM) model, with independent core tensor for ensemble effects and soft orthogonality for max-rank mapping, in addition to multi-partition embedding. MEIM improves expressiveness while still being highly efficient, helping it to outperform strong baselines and achieve state-of-the-art results on difficult link prediction benchmarks using fairly small embedding sizes. The source code is released at https://github.com/tranhungnghiep/MEIM-KGE.

Real AI is not data engineering or coding and software engineering skills, in big data tools or developer's skills in Python, R, Java, MATLAB, C or any other programming language desired, combined with machine learning skills. Keep a big view of Real AI as growing via three human intelligence faking levels to the Trans-AI: Artificial Narrow Intelligence (ANI)/ML/DLNNs; Artificial General Intelligence (AGI)/Human-Level AI; Artificial Super Intelligence (ASI); Trans-AI, Real and True AI, Meta-AI, Causal Machine Intelligence and Learning Man-Machine Hyperintelligence, the most disruptive integrative general-purpose technology.

Much of the success of deep learning is drawn from building architectures that properly respect underlying symmetry and structure in the data on which they operate - a set of considerations that have been united under the banner of geometric deep learning. Often problems in the physical sciences deal with relatively small sets of points in two- or three-dimensional space wherein translation, rotation, and permutation equivariance are important or even vital for models to be useful in practice. In this work, we present rotation- and permutation-equivariant architectures for deep learning on these small point clouds, composed of a set of products of terms from the geometric algebra and reductions over those products using an attention mechanism. The geometric algebra provides valuable mathematical structure by which to combine vector, scalar, and other types of geometric inputs in a systematic way to account for rotation invariance or covariance, while attention yields a powerful way to impose permutation equivariance. We demonstrate the usefulness of these architectures by training models to solve sample problems relevant to physics, chemistry, and biology.

Portfolio optimization has been an area of research that has attracted a lot of attention from researchers and financial analysts. Designing an optimum portfolio is a complex task since it not only involves accurate forecasting of future stock returns and risks but also needs to optimize them. This paper presents a systematic approach to portfolio optimization using two approaches, the hierarchical risk parity algorithm and the Eigen portfolio on seven sectors of the Indian stock market. The portfolios are built following the two approaches to historical stock prices from Jan 1, 2016, to Dec 31, 2020. The portfolio performances are evaluated on the test data from Jan 1, 2021, to Nov 1, 2021. The backtesting results of the portfolios indicate that the performance of the HRP portfolio is superior to that of its Eigen counterpart on both training and test data for the majority of the sectors studied.

The $k$ nearest neighbor algorithm ($k$NN) is one of the most popular nonparametric methods used for various purposes, such as treatment effect estimation, missing value imputation, classification, and clustering. The main advantage of $k$NN is its simplicity of hyperparameter optimization. It often produces favorable results with minimal effort. This paper proposes a generic semiparametric (or nonparametric if required) approach named Local Resampler (LR). LR utilizes $k$NN to create subsamples from the original sample and then generates synthetic values that are drawn from locally estimated distributions. LR can accurately create synthetic samples, even if the original sample has a non-convex distribution. Moreover, LR shows better or similar performance to other popular synthetic data methods with minimal model optimization with parametric distributional assumptions.

Functional data clustering is to identify heterogeneous morphological patterns in the continuous functions underlying the discrete measurements/observations. Application of functional data clustering has appeared in many publications across various fields of sciences, including but not limited to biology, (bio)chemistry, engineering, environmental science, medical science, psychology, social science, etc. The phenomenal growth of the application of functional data clustering indicates the urgent need for a systematic approach to develop efficient clustering methods and scalable algorithmic implementations. On the other hand, there is abundant literature on the cluster analysis of time series, trajectory data, spatio-temporal data, etc., which are all related to functional data. Therefore, an overarching structure of existing functional data clustering methods will enable the cross-pollination of ideas across various research fields. We here conduct a comprehensive review of original clustering methods for functional data. We propose a systematic taxonomy that explores the connections and differences among the existing functional data clustering methods and relates them to the conventional multivariate clustering methods. The structure of the taxonomy is built on three main attributes of a functional data clustering method and therefore is more reliable than existing categorizations. The review aims to bridge the gap between the functional data analysis community and the clustering community and to generate new principles for functional data clustering.