We propose a novel approach to nonlinear functional regression, called the Mapping-to-Parameter function model, which addresses complex and nonlinear functional regression problems in parameter space by employing any supervised learning technique. Central to this model is the mapping of function data from an infinite-dimensional function space to a finite-dimensional parameter space. This is accomplished by concurrently approximating multiple functions with a common set of B-spline basis functions by any chosen order, with their knot distribution determined by the Iterative Local Placement Algorithm, a newly proposed free knot placement algorithm. In contrast to the conventional equidistant knot placement strategy that uniformly distributes knot locations based on a predefined number of knots, our proposed algorithms determine knot location according to the local complexity of the input or output functions. The performance of our knot placement algorithms is shown to be robust in both single-function approximation and multiple-function approximation contexts. Furthermore, the effectiveness and advantage of the proposed prediction model in handling both function-on-scalar regression and function-on-function regression problems are demonstrated through several real data applications, in comparison with four groups of state-of-the-art methods.

Disaggregated evaluation is a central task in AI fairness assessment, with the goal to measure an AI system's performance across different subgroups defined by combinations of demographic or other sensitive attributes. The standard approach is to stratify the evaluation data across subgroups and compute performance metrics separately for each group. However, even for moderately-sized evaluation datasets, sample sizes quickly get small once considering intersectional subgroups, which greatly limits the extent to which intersectional groups are considered in many disaggregated evaluations. In this work, we introduce a structured regression approach to disaggregated evaluation that we demonstrate can yield reliable system performance estimates even for very small subgroups. We also provide corresponding inference strategies for constructing confidence intervals and explore how goodness-of-fit testing can yield insight into the structure of fairness-related harms experienced by intersectional groups. We evaluate our approach on two publicly available datasets, and several variants of semi-synthetic data. The results show that our method is considerably more accurate than the standard approach, especially for small subgroups, and goodness-of-fit testing helps identify the key factors that drive differences in performance.

Despite the rapid development of machine learning algorithms for domain generalization (DG), there is no clear empirical evidence that the existing DG algorithms outperform the classic empirical risk minimization (ERM) across standard benchmarks. To better understand this phenomenon, we investigate whether there are benefits of DG algorithms over ERM through the lens of label noise. Specifically, our finite-sample analysis reveals that label noise exacerbates the effect of spurious correlations for ERM, undermining generalization. Conversely, we illustrate that DG algorithms exhibit implicit label-noise robustness during finite-sample training even when spurious correlation is present. Such desirable property helps mitigate spurious correlations and improve generalization in synthetic experiments. However, additional comprehensive experiments on real-world benchmark datasets indicate that label-noise robustness does not necessarily translate to better performance compared to ERM. We conjecture that the failure mode of ERM arising from spurious correlations may be less pronounced in practice.

The task of predicting conversion rates (CVR) lies at the heart of online advertising systems aiming to optimize bids to meet advertiser performance requirements. Even with the recent rise of deep neural networks, these predictions are often made by factorization machines (FM), especially in commercial settings where inference latency is key. These models are trained using the logistic regression framework on labeled tabular data formed from past user activity that is relevant to the task at hand. Many advertisers only care about click-attributed conversions. A major challenge in training models that predict conversions-given-clicks comes from data sparsity - clicks are rare, conversions attributed to clicks are even rarer. However, mitigating sparsity by adding conversions that are not click-attributed to the training set impairs model calibration. Since calibration is critical to achieving advertiser goals, this is infeasible. In this work we use the well-known idea of self-supervised pre-training, and use an auxiliary auto-encoder model trained on all conversion events, both click-attributed and not, as a feature extractor to enrich the main CVR prediction model. Since the main model does not train on non click-attributed conversions, this does not impair calibration. We adapt the basic self-supervised pre-training idea to our online advertising setup by using a loss function designed for tabular data, facilitating continual learning by ensuring auto-encoder stability, and incorporating a neural network into a large-scale real-time ad auction that ranks tens of thousands of ads, under strict latency constraints, and without incurring a major engineering cost. We show improvements both offline, during training, and in an online A/B test. Following its success in A/B tests, our solution is now fully deployed to the Yahoo native advertising system.

A system of differential-algebraic equations (DAEs) is a combination of differential equations and algebraic equations, in which the differential equations are related to the dynamical evolution of the system, and the algebraic equations are responsible for constraining the solutions that satisfy the differential and algebraic equations. DAEs serve as essential models for a wide array of physical phenomena. They find applications across various domains such as mechanical systems, electrical circuit simulations, chemical process modeling, dynamic system control, biological simulations, and control systems. Consequently, solving these intricate differential equations has remained a significant challenge for researchers. To address this, a range of techniques including numerical, analytical, and semi-analytical methods have been employed to tackle the complexities inherent in solving DAEs.

Wind power generated by wind has non-schedule nature due to stochastic nature of meteorological variable. Hence energy business and control of wind power generation requires prediction of wind speed (WS) from few seconds to different time steps in advance. To deal with prediction shortcomings, various WS prediction methods have been used. Predictive data mining offers variety of methods for WS predictions where artificial neural network (ANN) is one of the reliable and accurate methods. It is observed from the result of this study that ANN gives better accuracy in comparison conventional model. The accuracy of WS prediction models is found to be dependent on input parameters and architecture type algorithms utilized. So the selection of most relevant input parameters is important research area in WS predicton field. The objective of the paper is twofold: first extensive review of ANN for wind power and WS prediction is carried out. Discussion and analysis of feature selection using Relief Algorithm (RA) in WS prediction are considered for different Indian sites. RA identify atmospheric pressure, solar radiation and relative humidity are relevant input variables. Based on relevant input variables Cascade ANN model is developed and prediction accuracy is evaluated. It is found that root mean square error (RMSE) for comparison between predicted and measured WS for training and testing wind speed are found to be 1.44 m/s and 1.49 m/s respectively. The developed cascade ANN model can be used to predict wind speed for sites where there are not WS measuring instruments are installed in India.

This paper considers stochastic weakly convex optimization without the standard Lipschitz continuity assumption. Based on new adaptive regularization (stepsize) strategies, we show that a wide class of stochastic algorithms, including the stochastic subgradient method, preserve the $\mathcal{O} ( 1 / \sqrt{K})$ convergence rate with constant failure rate. Our analyses rest on rather weak assumptions: the Lipschitz parameter can be either bounded by a general growth function of $\|x\|$ or locally estimated through independent random samples.

The quantification of storm updrafts remains unavailable for operational forecasting despite their inherent importance to convection and its associated severe weather hazards. Updraft proxies, like overshooting top area from satellite images, have been linked to severe weather hazards but only relate to a limited portion of the total storm updraft. This study investigates if a machine learning model, namely U-Nets, can skillfully retrieve maximum vertical velocity and its areal extent from 3-dimensional gridded radar reflectivity alone. The machine learning model is trained using simulated radar reflectivity and vertical velocity from the National Severe Storm Laboratory's convection permitting Warn on Forecast System (WoFS). A parametric regression technique using the sinh-arcsinh-normal distribution is adapted to run with U-Nets, allowing for both deterministic and probabilistic predictions of maximum vertical velocity. The best models after hyperparameter search provided less than 50% root mean squared error, a coefficient of determination greater than 0.65 and an intersection over union (IoU) of more than 0.45 on the independent test set composed of WoFS data. Beyond the WoFS analysis, a case study was conducted using real radar data and corresponding dual-Doppler analyses of vertical velocity within a supercell. The U-Net consistently underestimates the dual-Doppler updraft speed estimates by 50$\%$. Meanwhile, the area of the 5 and 10 m s^-1 updraft cores show an IoU of 0.25. While the above statistics are not exceptional, the machine learning model enables quick distillation of 3D radar data that is related to the maximum vertical velocity which could be useful in assessing a storm's severe potential.

In continual learning, catastrophic forgetting is affected by multiple aspects of the tasks. Previous works have analyzed separately how forgetting is affected by either task similarity or overparameterization. In contrast, our paper examines how task similarity and overparameterization jointly affect forgetting in an analyzable model. Specifically, we focus on two-task continual linear regression, where the second task is a random orthogonal transformation of an arbitrary first task (an abstraction of random permutation tasks). We derive an exact analytical expression for the expected forgetting - and uncover a nuanced pattern. In highly overparameterized models, intermediate task similarity causes the most forgetting. However, near the interpolation threshold, forgetting decreases monotonically with the expected task similarity. We validate our findings with linear regression on synthetic data, and with neural networks on established permutation task benchmarks.

Hybrid variational quantum algorithms (VQAs) are promising for solving practical problems such as combinatorial optimization, quantum chemistry simulation, quantum machine learning, and quantum error correction on noisy quantum computers. However, with typical random ansatz or quantum alternating operator ansatz, derived variational quantum algorithms become a black box for model interpretation. In this paper we construct a quantum regression algorithm wherein the quantum state directly encodes the classical data table and the variational parameters correspond directly to the regression coefficients which are real numbers by construction, providing a high degree of model interpretability and minimal cost to optimize with the right expressiveness. Instead of assuming the state preparation is given by granted, we discuss the state preparation with different encoders and their time complexity and overall resource cost. We can take advantage of the encoded data structure to cut down the algorithm time complexity. To the best of our knowledge, we show for the first time explicitly how the linkage of the classical data structure can be taken advantage of directly through quantum subroutines by construction. For nonlinear regression, our algorithm can be extended by building nonlinear features into the training data as demonstrated by numerical results. In addition, we demonstrate that the model trainability is achievable only when the number of features $M$ is much less than the number of records $L$ for the encoded data structure to justify $L\gg M$ in our resource estimation.