This article introduces a new symbolic regression algorithm based on the SPINEX (Similarity-based Predictions with Explainable Neighbors Exploration) family. This new algorithm (SPINEX_SymbolicRegression) adopts a similarity-based approach to identifying high-merit expressions that satisfy accuracy- and structural similarity metrics. We conducted extensive benchmarking tests comparing SPINEX_SymbolicRegression to over 180 mathematical benchmarking functions from international problem sets that span randomly generated expressions and those based on real physical phenomena. Then, we evaluated the performance of the proposed algorithm in terms of accuracy, expression similarity in terms of presence operators and variables (as compared to the actual expressions), population size, and number of generations at convergence. The results indicate that SPINEX_SymbolicRegression consistently performs well and can, in some instances, outperform leading algorithms. In addition, the algorithm's explainability capabilities are highlighted through in-depth experiments.

Precursor concentration and solar radiation intensity determine the dynamic equilibrium between ozone creation and destruction. Tropospheric ozone is a dangerous pollutant that can lead to a number of health problems as well as environmental difficulties. In contrast, stratospheric ozone creates a protective ozone layer. Exposure to high levels of tropospheric ozone can cause a range of respiratory problems, including coughing, throat irritation, and worsening of asthma symptoms. Long-term exposure can lead to more severe health issues such as chronic respiratory diseases, reduced lung function, and increased mortality rates. Children, the elderly, and individuals with pre-existing health conditions are particularly vulnerable to the adverse effects of ozone. Ground-level ozone can also damage flora, which can result in decreased agricultural production, damage to forests, and a decline in biodiversity. It prevents plants from photosynthesizing, which slows down their growth and increases their vulnerability to pests, illnesses, and harsh weather condition.

In causal inference, many estimands of interest can be expressed as a linear functional of the outcome regression function; this includes, for example, average causal effects of static, dynamic and stochastic interventions. For learning such estimands, in this work, we propose novel debiased machine learning estimators that are doubly robust asymptotically linear, thus providing not only doubly robust consistency but also facilitating doubly robust inference (e.g., confidence intervals and hypothesis tests). To do so, we first establish a key link between calibration, a machine learning technique typically used in prediction and classification tasks, and the conditions needed to achieve doubly robust asymptotic linearity. We then introduce calibrated debiased machine learning (C-DML), a unified framework for doubly robust inference, and propose a specific C-DML estimator that integrates cross-fitting, isotonic calibration, and debiased machine learning estimation. A C-DML estimator maintains asymptotic linearity when either the outcome regression or the Riesz representer of the linear functional is estimated sufficiently well, allowing the other to be estimated at arbitrarily slow rates or even inconsistently. We propose a simple bootstrap-assisted approach for constructing doubly robust confidence intervals. Our theoretical and empirical results support the use of C-DML to mitigate bias arising from the inconsistent or slow estimation of nuisance functions.

Most ost Big Data datasets suffer from selection bias. For example, X (Twitter) training observations differ largely from the testing offline observations as individuals on Twitter are generally more educated, democratic or left-leaning. Therefore, one major obstacle to reliable estimation is the differences between training and testing data. How can researchers make use of such data even in the presence of non-ignorable selection mechanisms? A number of methods have been developed for this issue, such as distributionally robust optimization (DRO) or learning fairness. A possible avenue to reducing the effect of bias is meta-information. Researchers, being field exerts, might have prior information on the form and extent of selection bias affecting their dataset, and in which direction the selection might cause the estimate to change, e.g. over or under estimation. At the same time, there is no direct way to leverage these types of information in learning. I propose a loss function which takes into account two types of meta data information given by the researcher: quantity and direction (under or over sampling) of bias in the training set. Estimation with the proposed loss function is then implemented through a neural network, the directional Rockafellar-Uryasev (dRU) regression model. I test the dRU model on a biased training dataset, a Big Data online drawn electoral poll. I apply the proposed model using meta data information coherent with the political and sampling information obtained from previous studies. The results show that including meta information improves the electoral results predictions compared to a model that does not include them.

This paper presents Sparse Gradient Descent as a solution for variable selection in convex piecewise linear regression where the model is given as $\mathrm{max}\langle a_j^\star, x \rangle + b_j^\star$ for $j = 1,\dots,k$ where $x \in \mathbb R^d$ is the covariate vector. Here, $\{a_j^\star\}_{j=1}^k$ and $\{b_j^\star\}_{j=1}^k$ denote the ground-truth weight vectors and intercepts. A non-asymptotic local convergence analysis is provided for Sp-GD under sub-Gaussian noise when the covariate distribution satisfies sub-Gaussianity and anti-concentration property. When the model order and parameters are fixed, Sp-GD provides an $\epsilon$-accurate estimate given $\mathcal{O}(\max(\epsilon^{-2}\sigma_z^2,1)s\log(d/s))$ observations where $\sigma_z^2$ denotes the noise variance. This also implies the exact parameter recovery by Sp-GD from $\mathcal{O}(s\log(d/s))$ noise-free observations. Since optimizing the squared loss for sparse max-affine is non-convex, an initialization scheme is proposed to provide a suitable initial estimate within the basin of attraction for Sp-GD, i.e. sufficiently accurate to invoke the convergence guarantees. The initialization scheme uses sparse principal component analysis to estimate the subspace spanned by $\{ a_j^\star\}_{j=1}^k$ then applies an $r$-covering search to estimate the model parameters. A non-asymptotic analysis is presented for this initialization scheme when the covariates and noise samples follow Gaussian distributions. When the model order and parameters are fixed, this initialization scheme provides an $\epsilon$-accurate estimate given $\mathcal{O}(\epsilon^{-2}\max(\sigma_z^4,\sigma_z^2,1)s^2\log^4(d))$ observations. Numerical Monte Carlo results corroborate theoretical findings for Sp-GD and the initialization scheme.

The discovery of scientific laws from measurements is a significant intellectual milestone, and its motivation arises from the widespread occurrence of nonlinear dynamical systems in science and engineering. Understanding the governing equations, which often take the form of ordinary differential equations (ODEs), partial differential equations (PDEs), and stochastic differential equations (SDEs), is essential for accurate prediction, effective control, and informed decision-making [1, 2]. In many complex systems, the underlying dynamics remain poorly understood, which renders conventional modeling techniques based on first principles both challenging and, at times, intractable. To tackle the challenge of model discovery in dynamical systems, Sparse Identification of Nonlinear Dynamics (SINDy) [3] offers a data-driven solution. By the use of given measurements, SINDy constructs parsimonious models that capture the essential features of system dynamics without the need for detailed knowledge of the underlying physics. The strength of SINDy lies in its ability to identify sparse and interpretable models, based on the assumption that the system's dynamics can be represented as a sparse linear combination of candidate functions. This process involves iterative optimization through sparse regression [4] and the selection of the most relevant terms from a comprehensive library, which enables the discovery of governing equations that are both accurate and physically meaningful. Building on the idea of using sparse regression techniques to discover nonlinear dynamical systems, extensive research has been conducted to enhance the SINDy framework for various objectives or to apply it across diverse domains.

Efficient sampling from un-normalized target distributions is pivotal in scientific computing and machine learning. While neural samplers have demonstrated potential with a special emphasis on sampling efficiency, existing neural implicit samplers still have issues such as poor mode covering behavior, unstable training dynamics, and sub-optimal performances. To tackle these issues, in this paper, we introduce Denoising Fisher Training (DFT), a novel training approach for neural implicit samplers with theoretical guarantees. We frame the training problem as an objective of minimizing the Fisher divergence by deriving a tractable yet equivalent loss function, which marks a unique theoretical contribution to assessing the intractable Fisher divergences. DFT is empirically validated across diverse sampling benchmarks, including two-dimensional synthetic distribution, Bayesian logistic regression, and high-dimensional energy-based models (EBMs). Notably, in experiments with high-dimensional EBMs, our best one-step DFT neural sampler achieves results on par with MCMC methods with up to 200 sampling steps, leading to a substantially greater efficiency over 100 times higher. This result not only demonstrates the superior performance of DFT in handling complex high-dimensional sampling but also sheds light on efficient sampling methodologies across broader applications.

Image Quality of MRI brain scans is strongly influenced by within scanner head movements and the resulting image artifacts alter derived measures like brain volume and cortical thickness. Automated image quality assessment is key to controlling for confounding effects of poor image quality. In this study, we systematically test for the influence of image quality on univariate statistics and machine learning classification. We analyzed group effects of sex/gender on local brain volume and made predictions of sex/gender using logistic regression, while correcting for brain size. From three large publicly available datasets, two age and sex-balanced samples were derived to test the generalizability of the effect for pooled sample sizes of n=760 and n=1094. Results of the Bonferroni corrected t-tests over 3747 gray matter features showed a strong influence of low-quality data on the ability to find significant sex/gender differences for the smaller sample. Increasing sample size and more so image quality showed a stark increase in detecting significant effects in univariate group comparisons. For the classification of sex/gender using logistic regression, both increasing sample size and image quality had a marginal effect on the Area under the Receiver Operating Characteristic Curve for most datasets and subsamples. Our results suggest a more stringent quality control for univariate approaches than for multivariate classification with a leaning towards higher quality for classical group statistics and bigger sample sizes for machine learning applications in neuroimaging.

Recent methods in quantile regression have adopted a classification perspective to handle challenges posed by heteroscedastic, multimodal, or skewed data by quantizing outputs into fixed bins. Although these regression-as-classification frameworks can capture high-density prediction regions and bypass convex quantile constraints, they are restricted by quantization errors and the curse of dimensionality due to a constant number of bins per dimension. To address these limitations, we introduce a conformalized high-density quantile regression approach with a dynamically adaptive set of prototypes. Our method optimizes the set of prototypes by adaptively adding, deleting, and relocating quantization bins throughout the training process. Moreover, our conformal scheme provides valid coverage guarantees, focusing on regions with the highest probability density. Experiments across diverse datasets and dimensionalities confirm that our method consistently achieves high-quality prediction regions with enhanced coverage and robustness, all while utilizing fewer prototypes and memory, ensuring scalability to higher dimensions. The code is available at https://github.com/batuceng/max_quantile .

The applicability domain refers to the range of data for which the prediction of the predictive model is expected to be reliable and accurate and using a model outside its applicability domain can lead to incorrect results. The ability to define the regions in data space where a predictive model can be safely used is a necessary condition for having safer and more reliable predictions to assure the reliability of new predictions. However, defining the applicability domain of a model is a challenging problem, as there is no clear and universal definition or metric for it. This work aims to make the applicability domain more quantifiable and pragmatic. Eight applicability domain detection techniques were applied to seven regression models, trained on five different datasets, and their performance was benchmarked using a validation framework. We also propose a novel approach based on non-deterministic Bayesian neural networks to define the applicability domain of the model. Our method exhibited superior accuracy in defining the Applicability Domain compared to previous methods, highlighting its potential in this regard.