Understanding the business cycle is crucial for building economic stability, guiding business planning, and informing investment decisions. The business cycle refers to the recurring pattern of expansion and contraction in economic activity over time. Economic analysis is inherently complex, incorporating a myriad of factors (such as macroeconomic indicators, political decisions). This complexity makes it challenging to fully account for all variables when determining the current state of the economy and predicting its future trajectory in the upcoming months. The objective of this study is to investigate the capacity of machine learning models in automatically analyzing the state of the economic, with the goal of forecasting business phases (expansion, slowdown, recession and recovery) in the United States and the EuroZone. We compared three different machine learning approaches to classify the phases of the business cycle, and among them, the Multinomial Logistic Regression (MLR) achieved the best results. Specifically, MLR got the best results by achieving the accuracy of 65.25% (Top1) and 84.74% (Top2) for the EuroZone and 75% (Top1) and 92.14% (Top2) for the United States. These results demonstrate the potential of machine learning techniques to predict business cycles accurately, which can aid in making informed decisions in the fields of economics and finance.

The data augmentation (DA) algorithms are popular Markov chain Monte Carlo (MCMC) algorithms often used for sampling from intractable probability distributions. This review article comprehensively surveys DA MCMC algorithms, highlighting their theoretical foundations, methodological implementations, and diverse applications in frequentist and Bayesian statistics. The article discusses tools for studying the convergence properties of DA algorithms. Furthermore, it contains various strategies for accelerating the speed of convergence of the DA algorithms, different extensions of DA algorithms and outlines promising directions for future research. This paper aims to serve as a resource for researchers and practitioners seeking to leverage data augmentation techniques in MCMC algorithms by providing key insights and synthesizing recent developments.

In this paper, we introduce a novel theoretical framework for multi-task regression, applying random matrix theory to provide precise performance estimations, under high-dimensional, non-Gaussian data distributions. We formulate a multi-task optimization problem as a regularization technique to enable single-task models to leverage multi-task learning information. We derive a closed-form solution for multi-task optimization in the context of linear models. Our analysis provides valuable insights by linking the multi-task learning performance to various model statistics such as raw data covariances, signal-generating hyperplanes, noise levels, as well as the size and number of datasets. We finally propose a consistent estimation of training and testing errors, thereby offering a robust foundation for hyperparameter optimization in multi-task regression scenarios. Experimental validations on both synthetic and real-world datasets in regression and multivariate time series forecasting demonstrate improvements on univariate models, incorporating our method into the training loss and thus leveraging multivariate information.

Mean-field Langevin dynamics (MFLD) minimizes an entropy-regularized nonlinear convex functional defined over the space of probability distributions. MFLD has gained attention due to its connection with noisy gradient descent for mean-field two-layer neural networks. Unlike standard Langevin dynamics, the nonlinearity of the objective functional induces particle interactions, necessitating multiple particles to approximate the dynamics in a finite-particle setting. Recent works (Chen et al., 2022; Suzuki et al., 2023b) have demonstrated the uniform-in-time propagation of chaos for MFLD, showing that the gap between the particle system and its mean-field limit uniformly shrinks over time as the number of particles increases. In this work, we improve the dependence on logarithmic Sobolev inequality (LSI) constants in their particle approximation errors, which can exponentially deteriorate with the regularization coefficient. Specifically, we establish an LSI-constant-free particle approximation error concerning the objective gap by leveraging the problem structure in risk minimization. As the application, we demonstrate improved convergence of MFLD, sampling guarantee for the mean-field stationary distribution, and uniform-in-time Wasserstein propagation of chaos in terms of particle complexity.

Certain cancer types, namely pancreatic cancer is difficult to detect at an early stage; sparking the importance of discovering the causal relationship between biomarkers and cancer to identify cancer efficiently. By allowing for the detection and monitoring of specific biomarkers through a non-invasive method, liquid biopsies enhance the precision and efficacy of medical interventions, advocating the move towards personalized healthcare. Several machine learning algorithms such as Random Forest, SVM are utilized for classification, yet causing inefficiency due to the need for conducting hyperparameter tuning. We leverage a meta-trained Hyperfast model for classifying cancer, accomplishing the highest AUC of 0.9929 and simultaneously achieving robustness especially on highly imbalanced datasets compared to other ML algorithms in several binary classification tasks (e.g. breast invasive carcinoma; BRCA vs. non-BRCA). We also propose a novel ensemble model combining pre-trained Hyperfast model, XGBoost, and LightGBM for multi-class classification tasks, achieving an incremental increase in accuracy (0.9464) while merely using 500 PCA features; distinguishable from previous studies where they used more than 2,000 features for similar results.

Randomised signature has been proposed as a flexible and easily implementable alternative to the well-established path signature. In this article, we employ randomised signature to introduce a generative model for financial time series data in the spirit of reservoir computing. Specifically, we propose a novel Wasserstein-type distance based on discrete-time randomised signatures. This metric on the space of probability measures captures the distance between (conditional) distributions. Its use is justified by our novel universal approximation results for randomised signatures on the space of continuous functions taking the underlying path as an input. We then use our metric as the loss function in a non-adversarial generator model for synthetic time series data based on a reservoir neural stochastic differential equation. We compare the results of our model to benchmarks from the existing literature.

Interest in bilevel optimization has grown in recent years, partially due to its applications to tackle challenging machine-learning problems. Several exciting recent works have been centered around developing efficient gradient-based algorithms that can solve bilevel optimization problems with provable guarantees. However, the existing literature mainly focuses on bilevel problems either without constraints, or featuring only simple constraints that do not couple variables across the upper and lower levels, excluding a range of complex applications. Our paper studies this challenging but less explored scenario and develops a (fully) first-order algorithm, which we term BLOCC, to tackle BiLevel Optimization problems with Coupled Constraints. We establish rigorous convergence theory for the proposed algorithm and demonstrate its effectiveness on two well-known real-world applications - hyperparameter selection in support vector machine (SVM) and infrastructure planning in transportation networks using the real data from the city of Seville.

Low-dimensional embeddings (LDEs) of high-dimensional data are ubiquitous in science and engineering. They allow us to quickly understand the main properties of the data, identify outliers and processing errors, and inform the next steps of data analysis. As such, LDEs have to be faithful to the original high-dimensional data, i.e., they should represent the relationships that are encoded in the data, both at a local as well as global scale. The current generation of LDE approaches focus on reconstructing local distances between any pair of samples correctly, often out-performing traditional approaches aiming at all distances. For these approaches, global relationships are, however, usually strongly distorted, often argued to be an inherent trade-off between local and global structure learning for embeddings. We suggest a new perspective on LDE learning, reconstructing angles between data points. We show that this approach, Mercat, yields good reconstruction across a diverse set of experiments and metrics, and preserve structures well across all scales. Compared to existing work, our approach also has a simple formulation, facilitating future theoretical analysis and algorithmic improvements.

Aero-engine fault prediction aims to accurately predict the development trend of the future state of aero-engines, so as to diagnose faults in advance. Traditional aero-engine parameter prediction methods mainly use the nonlinear mapping relationship of time series data but generally ignore the adequate spatiotemporal features contained in aero-engine data. To this end, we propose a brain-inspired spike echo state network (Spike-ESN) model for aero-engine intelligent fault prediction, which is used to effectively capture the evolution process of aero-engine time series data in the framework of spatiotemporal dynamics. In the proposed approach, we design a spike input layer based on Poisson distribution inspired by the spike neural encoding mechanism of biological neurons, which can extract the useful temporal characteristics in aero-engine sequence data. Then, the temporal characteristics are input into a spike reservoir through the current calculation method of spike accumulation in neurons, which projects the data into a high-dimensional sparse space. In addition, we use the ridge regression method to read out the internal state of the spike reservoir. Finally, the experimental results of aero-engine states prediction demonstrate the superiority and potential of the proposed method.

To develop rigorous knowledge about ML models -- and the systems in which they are embedded -- we need reliable measurements. But reliable measurement is fundamentally challenging, and touches on issues of reproducibility, scalability, uncertainty quantification, epistemology, and more. This dissertation addresses criteria needed to take reliability seriously: both criteria for designing meaningful metrics, and for methodologies that ensure that we can dependably and efficiently measure these metrics at scale and in practice. In doing so, this dissertation articulates a research vision for a new field of scholarship at the intersection of machine learning, law, and policy. Within this frame, we cover topics that fit under three different themes: (1) quantifying and mitigating sources of arbitrariness in ML, (2) taming randomness in uncertainty estimation and optimization algorithms, in order to achieve scalability without sacrificing reliability, and (3) providing methods for evaluating generative-AI systems, with specific focuses on quantifying memorization in language models and training latent diffusion models on open-licensed data. By making contributions in these three themes, this dissertation serves as an empirical proof by example that research on reliable measurement for machine learning is intimately and inescapably bound up with research in law and policy. These different disciplines pose similar research questions about reliable measurement in machine learning. They are, in fact, two complementary sides of the same research vision, which, broadly construed, aims to construct machine-learning systems that cohere with broader societal values.