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We present that, instead of establishing the equations of motion, one can model-freely reveal the dynamical properties of a black-box system using a learning machine. Trained only by a segment of time series of a state variable recorded at…
A new criterion for A-stability of peer two-step methods is presented which is verifiable exactly in exact arithmetic by checking semi-definiteness of a certain test matrix. It depends on the existence of two positive definite weight…
In a semi-supervised learning scenario, (possibly noisy) partially observed labels are used as input to train a classifier, in order to assign labels to unclassified samples. In this paper, we study this classifier learning problem from a…
The standard paradigm of cosmology assumes General Relativity (GR) is a valid theory for gravity at scales in which it has not been properly tested. Developing novel tests of GR and its alternatives is crucial if we want to give strength to…
We propose Geometric Pareto Control (GPC), a framework overcoming barriers of reinforcement learning in cyber-physical systems where governing physics is known. Reinforcement learning confronts barriers in safety-critical applications:…
We focus on the classification problem with a separable dataset, one of the most important and classical problems from machine learning. The standard approach to this task is logistic regression with gradient descent (LR+GD). Recent studies…
Leave-one-problem-out (LOPO) performance prediction requires machine learning (ML) models to extrapolate algorithms' performance from a set of training problems to a previously unseen problem. LOPO is a very challenging task even for…
The crucial but undocumented Dolan-McCrea variational method is richly applied. Using the said method, we analytically derived a field equation comprising entirely of geometric structures and we investigate how effectively it describes…
Estimation in generalized linear models (GLM) is complicated by the presence of constraints. One can handle constraints by maximizing a penalized log-likelihood. Penalties such as the lasso are effective in high dimensions, but often lead…
We consider the computational challenges associated with uncertainty quantification involved in parameter estimation such as seismic slowness and hydraulic transmissivity fields. The reconstruction of these parameters can be mathematically…
This paper introduces an iterative tomogravity algorithm for the estimation of a network traffic matrix based on one snapshot observation of the link loads in the network. The proposed method does not require complete observation of the…
This research presents a comprehensive framework for analyzing liquidity in financial markets, particularly in the context of high-frequency trading. By leveraging advanced machine learning classification techniques, including Logistic…
We design strategies in nonlinear geometric analysis to temper the effects of adversarial learning for sufficiently smooth data of numerical method-type dynamics in encoder-decoder methods, variational and deterministic, through the use of…
Often in real-world datasets, especially in high dimensional data, some feature values are missing. Since most data analysis and statistical methods do not handle gracefully missing values, the first step in the analysis requires the…
Fraud detection remains a critical task in high-stakes domains such as finance and e-commerce, where undetected fraudulent transactions can lead to significant economic losses. In this study, we systematically compare the performance of…
Error bound analysis, which estimates the distance of a point to the solution set of an optimization problem using the optimality residual, is a powerful tool for the analysis of first-order optimization algorithms. In this paper, we use…
Although machine learning approaches have been widely used in the field of finance, to very successful degrees, these approaches remain bespoke to specific investigations and opaque in terms of explainability, comparability, and…
Data in modern economic and financial applications often arrive as a stream, requiring models and inference to be updated in real time -- yet most semiparametric methods remain batch-based and computationally impractical in large-scale…
Inertial parameter identification of industrial robots is an established process, but standard methods using Least Squares or Machine Learning do not consider prior information about the robot and require extensive measurements. Inspired by…
The estimation problem in a high regression model with structured sparsity is investigated. An algorithm using a two steps block thresholding procedure called GR-LOL is provided. Convergence rates are produced: they depend on simple…