Regression algorithms are regularly used for improving the accuracy of satellite precipitation products. In this context, satellite precipitation and topography data are the predictor variables, and gauged-measured precipitation data are the dependent variables. Alongside this, it is increasingly recognised in many fields that combinations of algorithms through ensemble learning can lead to substantial predictive performance improvements. Still, a sufficient number of ensemble learners for improving the accuracy of satellite precipitation products and their large-scale comparison are currently missing from the literature. In this study, we work towards filling in this specific gap by proposing 11 new ensemble learners in the field and by extensively comparing them. We apply the ensemble learners to monthly data from the PERSIANN (Precipitation Estimation from Remotely Sensed Information using Artificial Neural Networks) and IMERG (Integrated Multi-satellitE Retrievals for GPM) gridded datasets that span over a 15-year period and over the entire the contiguous United States (CONUS). We also use gauge-measured precipitation data from the Global Historical Climatology Network monthly database, version 2 (GHCNm). The ensemble learners combine the predictions of six machine learning regression algorithms (base learners), namely the multivariate adaptive regression splines (MARS), multivariate adaptive polynomial splines (poly-MARS), random forests (RF), gradient boosting machines (GBM), extreme gradient boosting (XGBoost) and Bayesian regularized neural networks (BRNN), and each of them is based on a different combiner. The combiners include the equal-weight combiner, the median combiner, two best learners and seven variants of a sophisticated stacking method. The latter stacks a regression algorithm on top of the base learners to combine their independent predictions...

How does the formulation of a target variable affect performance within the ML pipeline? The experiments in this study examine numeric targets that have been binarized by comparing against a threshold. We compare the predictive performance of regression models trained to predict the numeric targets vs. classifiers trained to predict their binarized counterparts. Specifically, we make this comparison at every point of a randomized hyperparameter optimization search to understand the effect of computational resource budget on the tradeoff between the two. We find that regression requires significantly more computational effort to converge upon the optimal performance, and is more sensitive to both randomness and heuristic choices in the training process. Although classification can and does benefit from systematic hyperparameter tuning and model selection, the improvements are much less than for regression. This work comprises the first systematic comparison of regression and classification within the framework of computational resource requirements. Our findings contribute to calls for greater replicability and efficiency within the ML pipeline for the sake of building more sustainable and robust AI systems.

This research delves into the reduction of machine learning model bias through Ensemble Learning. Our rigorous methodology comprehensively assesses bias across various categorical variables, ultimately revealing a pronounced gender attribute bias. The empirical evidence unveils a substantial gender-based wage prediction disparity: wages predicted for males, initially at \$902.91, significantly decrease to \$774.31 when the gender attribute is alternated to females. Notably, Kullback-Leibler divergence scores point to gender bias, with values exceeding 0.13, predominantly within tree-based models. Employing Ensemble Learning elucidates the quest for fairness and transparency. Intriguingly, our findings reveal that the stacked model aligns with individual models, confirming the resilience of model bias. This study underscores ethical considerations and advocates the implementation of hybrid models for a data-driven society marked by impartiality and inclusivity.

The problems of Lasso regression and optimal design of experiments share a critical property: their optimal solutions are typically \emph{sparse}, i.e., only a small fraction of the optimal variables are non-zero. Therefore, the identification of the support of an optimal solution reduces the dimensionality of the problem and can yield a substantial simplification of the calculations. It has recently been shown that linear regression with a \emph{squared} $\ell_1$-norm sparsity-inducing penalty is equivalent to an optimal experimental design problem. In this work, we use this equivalence to derive safe screening rules that can be used to discard inessential samples. Compared to previously existing rules, the new tests are much faster to compute, especially for problems involving a parameter space of high dimension, and can be used dynamically within any iterative solver, with negligible computational overhead. Moreover, we show how an existing homotopy algorithm to compute the regularization path of the lasso method can be reparametrized with respect to the squared $\ell_1$-penalty. This allows the computation of a Bayes $c$-optimal design in a finite number of steps and can be several orders of magnitude faster than standard first-order algorithms. The efficiency of the new screening rules and of the homotopy algorithm are demonstrated on different examples based on real data.

Overparametrization often helps improve the generalization performance. This paper presents a dual view of overparametrization suggesting that downsampling may also help generalize. Focusing on the proportional regime $m\asymp n \asymp p$, where $m$ represents the sketching size, $n$ is the sample size, and $p$ is the feature dimensionality, we investigate two out-of-sample prediction risks of the sketched ridgeless least square estimator. Our findings challenge conventional beliefs by showing that downsampling does not always harm generalization but can actually improve it in certain cases. We identify the optimal sketching size that minimizes out-of-sample prediction risks and demonstrate that the optimally sketched estimator exhibits stabler risk curves, eliminating the peaks of those for the full-sample estimator. To facilitate practical implementation, we propose an empirical procedure to determine the optimal sketching size. Finally, we extend our analysis to cover central limit theorems and misspecified models. Numerical studies strongly support our theory.

High resolution tactile sensing has great potential in autonomous mobile robotics, particularly for legged robots. One particular area where it has significant promise is the traversal of challenging, varied terrain. Depending on whether an environment is slippery, soft, hard or dry, a robot must adapt its method of locomotion accordingly. Currently many multi-legged robots, such as Boston Dynamic's Spot robot, have preset gaits for different surface types, but struggle over terrains where the surface type changes frequently. Being able to automatically detect changes within an environment would allow a robot to autonomously adjust its method of locomotion to better suit conditions, without requiring a human user to manually set the change in surface type. In this paper we report on the first detailed investigation of the properties of a particular bio-inspired tactile sensor, the TacTip, to test its suitability for this kind of automatic detection of surface conditions. We explored different processing techniques and a regression model, using a custom made rig for data collection to determine how a robot could sense directional and general force on the sensor in a variety of conditions. This allowed us to successfully demonstrate how the sensor can be used to distinguish between soft, hard, dry and (wet) slippery surfaces. We further explored a neural model to classify specific surface textures. Pin movement (the movement of optical markers within the sensor) was key to sensing this information, and all models relied on some form of temporal information. Our final trained models could successfully determine the direction the sensor is heading in, the amount of force acting on it, and determine differences in the surface texture such as Lego vs smooth hard surface, or concrete vs smooth hard surface.

We propose a novel surrogate modelling approach to efficiently and accurately approximate the response of complex dynamical systems driven by time-varying exogenous excitations over extended time periods. Our approach, namely manifold nonlinear autoregressive modelling with exogenous input (mNARX), involves constructing a problem-specific exogenous input manifold that is optimal for constructing autoregressive surrogates. The manifold, which forms the core of mNARX, is constructed incrementally by incorporating the physics of the system, as well as prior expert- and domain- knowledge. Because mNARX decomposes the full problem into a series of smaller sub-problems, each with a lower complexity than the original, it scales well with the complexity of the problem, both in terms of training and evaluation costs of the final surrogate. Furthermore, mNARX synergizes well with traditional dimensionality reduction techniques, making it highly suitable for modelling dynamical systems with high-dimensional exogenous inputs, a class of problems that is typically challenging to solve. Since domain knowledge is particularly abundant in physical systems, such as those found in civil and mechanical engineering, mNARX is well suited for these applications. We demonstrate that mNARX outperforms traditional autoregressive surrogates in predicting the response of a classical coupled spring-mass system excited by a one-dimensional random excitation. Additionally, we show that mNARX is well suited for emulating very high-dimensional time- and state-dependent systems, even when affected by active controllers, by surrogating the dynamics of a realistic aero-servo-elastic onshore wind turbine simulator. In general, our results demonstrate that mNARX offers promising prospects for modelling complex dynamical systems, in terms of accuracy and efficiency.

Transformer-based large language models (Vaswani et al., 2017) pretrained with diverse tasks have demonstrated strong ability for in-context learning (ICL), that is, the pretrained models can answer new queries based on a few in-context demonstrations (see, e.g., Brown et al. (2020) and references thereafter). ICL is one of the key abilities contributing to the success of large language models, which allows pretrained models to solve multiple downstream tasks without updating their model parameters. However, the statistical foundation of ICL is still in its infancy. A recent line of research aims to quantify ICL by studying transformers pretrained on the linear regression task with a Gaussian prior (Garg et al., 2022; Akyürek et al., 2022; Li et al., 2023b; Raventós et al., 2023). Specifically, Garg et al. (2022); Akyürek et al. (2022); Li et al. (2023b) study the setting where transformers are pretrained in an online manner using independent linear regression tasks with the same Gaussian prior. They find that such a pretrained transformer can perform ICL on fresh linear regression tasks.

Many causal estimands are only partially identifiable since they depend on the unobservable joint distribution between potential outcomes. Stratification on pretreatment covariates can yield sharper partial identification bounds; however, unless the covariates are discrete with relatively small support, this approach typically requires consistent estimation of the conditional distributions of the potential outcomes given the covariates. Thus, existing approaches may fail under model misspecification or if consistency assumptions are violated. In this study, we propose a unified and model-agnostic inferential approach for a wide class of partially identified estimands, based on duality theory for optimal transport problems. In randomized experiments, our approach can wrap around any estimates of the conditional distributions and provide uniformly valid inference, even if the initial estimates are arbitrarily inaccurate. Also, our approach is doubly robust in observational studies. Notably, this property allows analysts to use the multiplier bootstrap to select covariates and models without sacrificing validity even if the true model is not included. Furthermore, if the conditional distributions are estimated at semiparametric rates, our approach matches the performance of an oracle with perfect knowledge of the outcome model. Finally, we propose an efficient computational framework, enabling implementation on many practical problems in causal inference.

Over-parameterized models like deep nets and random forests have become very popular in machine learning. However, the natural goals of continuity and differentiability, common in regression models, are now often ignored in modern overparametrized, locally-adaptive models. We propose a general framework to construct a global continuous and differentiable model based on a weighted average of locally learned models in corresponding local regions. This model is competitive in dealing with data with different densities or scales of function values in different local regions. We demonstrate that when we mix kernel ridge and polynomial regression terms in the local models, and stitch them together continuously, we achieve faster statistical convergence in theory and improved performance in various practical settings.