A Simple Method for Robust Regression

Evaluating future water availability in Texas through the lens of a data-driven approach leveraged with CMIP6 general circulation models

Climate change is escalating the frequency and intensity of extreme precipitation events, significantly influencing the spatial and temporal distributions of water resources. This is particularly evident in Texas, a rapidly growing state with a pronounced west-east gradient in water supply. This study utilizes Coupled Model Intercomparison Project Phase 6 (CMIP6) data and data-driven methodology to improve projections of Texas's future water resources, focusing on actual evapotranspiration (AET) and water availability through enhanced Multi-Model Ensembles. The results reveal that the data-driven model significantly outperforms the CMIP5 and CMIP6 models across all skill metrics, underscoring the potential of data-driven methodologies in advancing climate science. Furthermore, the study provides an in-depth analysis of the projected changes in net water availability (NWA) and estimated water demand for different regions in Texas over the next six decades from 2015 to 2074, which reveal fluctuating patterns of water stress, with the regions (nine out of sixteen water planning regions in Texas, especially for the most populated regions) poised for heightened challenges in reconciling water demand and availability. While increasing trends are found in precipitation, AET, and NWA for the northern region of Texas based on SSP2-4.5, decreasing trends are found over the southern region for all three parameters based on SSP5-8.5. These findings underscore the importance of factoring both spatial and temporal variations in water availability and demand for effective water management strategies and the need for adaptive water management strategies for the changing water availability scenarios.

A Framework of Learning Through Empirical Gain Maximization

We develop in this letter a framework of empirical gain maximization (EGM) to address the robust regression problem where heavy-tailed noise or outliers may be present in the response variable. The idea of EGM is to approximate the density function of the noise distribution instead of approximating the truth function directly as usual. Unlike the classical maximum likelihood estimation that encourages equal importance of all observations and could be problematic in the presence of abnormal observations, EGM schemes can be interpreted from a minimum distance estimation viewpoint and allow the ignorance of those observations. Furthermore, we show that several well-known robust nonconvex regression paradigms, such as Tukey regression and truncated least square regression, can be reformulated into this new framework. We then develop a learning theory for EGM by means of which a unified analysis can be conducted for these well-established but not fully understood regression approaches. This new framework leads to a novel interpretation of existing bounded nonconvex loss functions. Within this new framework, the two seemingly irrelevant terminologies, the well-known Tukey's biweight loss for robust regression and the triweight kernel for nonparametric smoothing, are closely related. More precisely, we show that Tukey's biweight loss can be derived from the triweight kernel. Other frequently employed bounded nonconvex loss functions in machine learning, such as the truncated square loss, the Geman-McClure loss, and the exponential squared loss, can also be reformulated from certain smoothing kernels in statistics. In addition, the new framework enables us to devise new bounded nonconvex loss functions for robust learning.

Regularization Methods Based on the Lq-Likelihood for Linear Models with Heavy-Tailed Errors

We propose regularization methods for linear models based on the Lq-likelihood, which is a generalization of the log-likelihood using a power function. Regularization methods are popular for the estimation in the normal linear model. However, heavy-tailed errors are also important in statistics and machine learning. We assume q-normal distributions as the errors in linear models. A q-normal distribution is heavy-tailed, which is defined using a power function, not the exponential function. We find that the proposed methods for linear models with q-normal errors coincide with the ordinary regularization methods that are applied to the normal linear model. The proposed methods can be computed using existing packages because they are penalized least squares methods. We examine the proposed methods using numerical experiments, showing that the methods perform well, even when the error is heavy-tailed. The numerical experiments also illustrate that our methods work well in model selection and generalization, especially when the error is slightly heavy-tailed.

Linking alpha oscillations, attention and inhibitory control in adult ADHD with EEG neurofeedback

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Resting alpha power is reduced in adult ADHD suggesting cortical hyper-activation.

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Adult ADHD patients successfully reduce alpha power during neurofeedback.

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A post-neurofeedback rebound normalizes alpha power in adult ADHD.

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Alpha power rebound correlates with improvement of inhibitory control in adult ADHD.

Abnormal patterns of electrical oscillatory activity have been repeatedly described in adult ADHD. In particular, the alpha rhythm (8–12 Hz), known to be modulated during attention, has previously been considered as candidate biomarker for ADHD. In the present study, we asked adult ADHD patients to self-regulate their own alpha rhythm using neurofeedback (NFB), in order to examine the modulation of alpha oscillations on attentional performance and brain plasticity. Twenty-five adult ADHD patients and 22 healthy controls underwent a 64-channel EEG-recording at resting-state and during a Go/NoGo task, before and after a 30 min-NFB session designed to reduce (desynchronize) the power of the alpha rhythm. Alpha power was compared across conditions and groups, and the effects of NFB were statistically assessed by comparing behavioral and EEG measures pre-to-post NFB. Firstly, we found that relative alpha power was attenuated in our ADHD cohort compared to control subjects at baseline and across experimental conditions, suggesting a signature of cortical hyper-activation. Both groups demonstrated a significant and targeted reduction of alpha power during NFB. Interestingly, we observed a post-NFB increase in resting-state alpha (i.e. rebound) in the ADHD group, which restored alpha power towards levels of the normal population. Importantly, the degree of post-NFB alpha normalization during the Go/NoGo task correlated with individual improvements in motor inhibition (i.e. reduced commission errors) only in the ADHD group. Overall, our findings offer novel supporting evidence implicating alpha oscillations in inhibitory control, as well as their potential role in the homeostatic regulation of cortical excitatory/inhibitory balance.

A robot-assisted imaging pipeline for tracking the growths of maize ear and silks in a high-throughput phenotyping platform

BACKGROUND

In maize, silks are hundreds of filaments that simultaneously emerge from the ear for collecting pollen over a period of 1-7 days, which largely determines grain number especially under water deficit. Silk growth is a major trait for drought tolerance in maize, but its phenotyping is difficult at throughputs needed for genetic analyses.

RESULTS

We have developed a reproducible pipeline that follows ear and silk growths every day for hundreds of plants, based on an ear detection algorithm that drives a robotized camera for obtaining detailed images of ears and silks. We first select, among 12 whole-plant side views, those best suited for detecting ear position. Images are segmented, the stem pixels are labelled and the ear position is identified based on changes in width along the stem. A mobile camera is then automatically positioned in real time at 30 cm from the ear, for a detailed picture in which silks are identified based on texture and colour. This allows analysis of the time course of ear and silk growths of thousands of plants. The pipeline was tested on a panel of 60 maize hybrids in the PHENOARCH phenotyping platform. Over 360 plants, ear position was correctly estimated in 86% of cases, before it could be visually assessed. Silk growth rate, estimated on all plants, decreased with time consistent with literature. The pipeline allowed clear identification of the effects of genotypes and water deficit on the rate and duration of silk growth.

CONCLUSIONS

The pipeline presented here, which combines computer vision, machine learning and robotics, provides a powerful tool for large-scale genetic analyses of the control of reproductive growth to changes in environmental conditions in a non-invasive and automatized way. It is available as Open Source software in the OpenAlea platform.