Abstract--In this paper, we investigate meta-learning for combining forecasts generated by models of different types . While typical approaches for combining forecasts involve s imple averaging, machine learning techniques enable more sophis ti-cated methods of combining through meta-learning, leading to improved forecasting accuracy. We use linear regression, k - nearest neighbors, multilayer perceptron, random forest, and long short-term memory as meta-learners. We define global and local meta-learning variants for time series with compl ex seasonality and compare meta-learners on multiple forecas ting problems, demonstrating their superior performance compa red to simple averaging. Ensemble methods are widely recognized as a cornerstone of modern machine learning (ML) [1], commonly used for regression and classification problems. In addition, ensem bling has proven to be a highly effective approach for increasing the predictive power of forecasting models. The ensemble approach in forecasting, which involves combining the predictions of multiple models, can be justified for several reasons. First of all, it usually leads to increased accurac y. Ensemble models often outperform individual models, as the y leverage the strengths of different models and minimize the ir weaknesses. By combining diverse models, the ensemble can produce more accurate predictions by capturing a broader range of patterns and insights from the data. Ensembling als o allows for the incorporation of multiple drivers into the da ta generating process, mitigating uncertainties regarding m odel form and parameter specification [2].

I show that ordinary least squares (OLS) predictions can be rewritten as the output of a restricted attention module, akin to those forming the backbone of large language models. This connection offers an alternative perspective on attention beyond the conventional information retrieval framework, making it more accessible to researchers and analysts with a background in traditional statistics. It falls into place when OLS is framed as a similarity-based method in a transformed regressor space, distinct from the standard view based on partial correlations. In fact, the OLS solution can be recast as the outcome of an alternative problem: minimizing squared prediction errors by optimizing the embedding space in which training and test vectors are compared via inner products. Rather than estimating coefficients directly, we equivalently learn optimal encoding and decoding operations for predictors. From this vantage point, OLS maps naturally onto the query-key-value structure of attention mechanisms. Building on this foundation, I discuss key elements of Transformer-style attention and draw connections to classic ideas from time series econometrics.

Fruit drying is widely used in food manufacturing to reduce product moisture, ensure product safety, and extend product shelf life. Accurately predicting final moisture content (MC) is critically needed for quality control of drying processes. State-of-the-art methods can build deterministic relationships between process parameters and MC, but cannot adequately account for inherent process variabilities that are ubiquitous in fruit drying. To address this gap, this paper presents a novel multi-modal data fusion framework to effectively fuse two modalities of data: tabular data (process parameters) and high-dimensional image data (images of dried apple slices) to enable accurate MC prediction. The proposed modeling architecture permits flexible adjustment of information portion from tabular and image data modalities. Experimental validation shows that the multi-modal approach improves predictive accuracy substantially compared to state-of-the-art methods. The proposed method reduces root-mean-squared errors by 19.3%, 24.2%, and 15.2% over tabular-only, image-only, and standard tabular-image fusion models, respectively. Furthermore, it is demonstrated that our method is robust in varied tabular-image ratios and capable of effectively capturing inherent small-scale process variabilities. The proposed framework is extensible to a variety of other drying technologies.

This study reveals the important role of prevention care and medication adherence in reducing hospitalizations. By using a structured dataset of 1,171 patients, four machine learning models Logistic Regression, Gradient Boosting, Random Forest, and Artificial Neural Networks are applied to predict five-year hospitalization risk, with the Gradient Boosting model achieving the highest accuracy of 81.2%. The result demonstrated that patients with high medication adherence and consistent preventive care can reduce 38.3% and 37.7% in hospitalization risk. The finding also suggests that targeted preventive care can have positive Return on Investment (ROI), and therefore ML models can effectively direct personalized interventions and contribute to long-term medical savings.

The correlation matrix is a central representation of functional brain networks in neuroimaging. Traditional analyses often treat pairwise interactions independently in a Euclidean setting, overlooking the intrinsic geometry of correlation matrices. While earlier attempts have embraced the quotient geometry of the correlation manifold, they remain limited by computational inefficiency and numerical instability, particularly in high-dimensional contexts. This paper presents a novel geometric framework that employs diffeomorphic transformations to embed correlation matrices into a Euclidean space, preserving salient manifold properties and enabling large-scale analyses. The proposed method integrates with established learning algorithms - regression, dimensionality reduction, and clustering - and extends naturally to population-level inference of brain networks. Simulation studies demonstrate both improved computational speed and enhanced accuracy compared to conventional manifold-based approaches. Moreover, applications in real neuroimaging scenarios illustrate the framework's utility, enhancing behavior score prediction, subject fingerprinting in resting-state fMRI, and hypothesis testing in electroencephalogram data. An open-source MATLAB toolbox is provided to facilitate broader adoption and advance the application of correlation geometry in functional brain network research.

A foundational framework within the literature on inflation dynamics is the Phillips Curve (PC) model. The Phillips Curve posits a short-term trade-off between inflation and a measure of economic slack, typically proxied by unemployment rate, such that higher inflation is associated with lower slack in the economy and vice-versa. The earliest empirical validation of this relationship, based on wage inflation and unemployment rate was provided by Phillips (1958) for the United Kingdom. Since then, the Phillips Curve framework has undergone significant theoretical advancements, culminating in the development of the micro-founded New Keynesian Phillips Curve (NKPC) (Taylor, 1980; Calvo, 1983a; Gali and Gertler, 1999) as the workhorse model for inflation analysis. Despite its theoretical appeal, the practical application of the NKPC for inflation modelling and forecasting--particularly within central banks--has been fraught with challenges. Such difficulties stem from structural breaks, state dependencies, and intrinsic nonlinearities in the relationship between inflation and its fundamental determinants, complicating its empirical validity and predictive performance (see Cristini and Ferri, 2021).

Sparsified Learning is ubiquitous in many machine learning tasks. It aims to regularize the objective function by adding a penalization term that considers the constraints made on the learned parameters. This paper considers the problem of learning heavy-tailed LSP. We develop a flexible and robust sparse learning framework capable of handling heavy-tailed data with locally stationary behavior and propose concentration inequalities. We further provide non-asymptotic oracle inequalities for different types of sparsity, including $\ell_1$-norm and total variation penalization for the least square loss.

We review the literature on algorithms for estimating the in dex space in a multi-index model. The primary focus is on computa tionally efficient (polynomial-time) algorithms in Gaussian space, the assumptions under which consistency is guaranteed by these methods, and their sample complexity. In many cases, a gap is observed between the sample c omplexity of the best known computationally efficient methods and the i nformation-theoretical minimum. We also review algorithms based on est imating the span of gradients using nonparametric methods, and algorit hms based on fitting neural networks using gradient descent.

We revisit the problem of estimating $k$ linear regressors with self-selection bias in $d$ dimensions with the maximum selection criterion, as introduced by Cherapanamjeri, Daskalakis, Ilyas, and Zampetakis [CDIZ23, STOC'23]. Our main result is a $\operatorname{poly}(d,k,1/\varepsilon) + {k}^{O(k)}$ time algorithm for this problem, which yields an improvement in the running time of the algorithms of [CDIZ23] and [GM24, arXiv]. We achieve this by providing the first local convergence algorithm for self-selection, thus resolving the main open question of [CDIZ23]. To obtain this algorithm, we reduce self-selection to a seemingly unrelated statistical problem called coarsening. Coarsening occurs when one does not observe the exact value of the sample but only some set (a subset of the sample space) that contains the exact value. Inference from coarse samples arises in various real-world applications due to rounding by humans and algorithms, limited precision of instruments, and lag in multi-agent systems. Our reduction to coarsening is intuitive and relies on the geometry of the self-selection problem, which enables us to bypass the limitations of previous analytic approaches. To demonstrate its applicability, we provide a local convergence algorithm for linear regression under another self-selection criterion, which is related to second-price auction data. Further, we give the first polynomial time local convergence algorithm for coarse Gaussian mean estimation given samples generated from a convex partition. Previously, only a sample-efficient algorithm was known due to Fotakis, Kalavasis, Kontonis, and Tzamos [FKKT21, COLT'21].

Recently, linear regression models incorporating an optimal transport (OT) loss have been explored for applications such as supervised unmixing of spectra, music transcription, and mass spectrometry. However, these task-specific approaches often do not generalize readily to a broader class of linear models. In this work, we propose a novel algorithmic framework for solving a general class of non-negative linear regression models with an entropy-regularized OT datafit term, based on Sinkhorn-like scaling iterations. Our framework accommodates convex penalty functions on the weights (e.g. squared-$\ell_2$ and $\ell_1$ norms), and admits additional convex loss terms between the transported marginal and target distribution (e.g. squared error or total variation). We derive simple multiplicative updates for common penalty and datafit terms. This method is suitable for large-scale problems due to its simplicity of implementation and straightforward parallelization.