Random forest is an important method for ML applications due to its broad outperformance over competing methods for structured tabular data. We propose a method for transfer learning in nonparametric regression using a centered random forest (CRF) with distance covariance-based feature weights, assuming the unknown source and target regression functions are different for a few features (sparsely different). Our method first obtains residuals from predicting the response in the target domain using a source domain-trained CRF. Then, we fit another CRF to the residuals, but with feature splitting probabilities proportional to the sample distance covariance between the features and the residuals in an independent sample. We derive an upper bound on the mean square error rate of the procedure as a function of sample sizes and difference dimension, theoretically demonstrating transfer learning benefits in random forests. In simulations, we show that the results obtained for the CRFs also hold numerically for the standard random forest (SRF) method with data-driven feature split selection. Beyond transfer learning, our results also show the benefit of distance-covariance-based weights on the performance of RF in some situations. Our method shows significant gains in predicting the mortality of ICU patients in smaller-bed target hospitals using a large multi-hospital dataset of electronic health records for 200,000 ICU patients.

Dataset bias often leads deep learning models to exploit spurious correlations instead of task-relevant signals. We introduce the Standard Anti-Causal Model (SAM), a unifying causal framework that characterizes bias mechanisms and yields a conditional independence criterion for causal stability. Building on this theory, we propose DISCO$_m$ and sDISCO, efficient and scalable estimators of conditional distance correlation that enable independence regularization in black-box models. Across five diverse datasets, our methods consistently outperform or are competitive in existing bias mitigation approaches, while requiring fewer hyperparameters and scaling seamlessly to multi-bias scenarios. This work bridges causal theory and practical deep learning, providing both a principled foundation and effective tools for robust prediction. Source Code: https://github.com/***.

Ensuring equitable treatment (fairness) across protected attributes (such as gender or ethnicity) is a critical issue in machine learning. Most existing literature focuses on binary classification, but achieving fairness in regression tasks-such as insurance pricing or hiring score assessments-is equally important. Moreover, anti-discrimination laws also apply to continuous attributes, such as age, for which many existing methods are not applicable. In practice, multiple protected attributes can exist simultaneously; however, methods targeting fairness across several attributes often overlook so-called "fairness gerrymandering", thereby ignoring disparities among intersectional subgroups (e.g., African-American women or Hispanic men). In this paper, we propose a distance covariance regularisation framework that mitigates the association between model predictions and protected attributes, in line with the fairness definition of demographic parity, and that captures both linear and nonlinear dependencies. To enhance applicability in the presence of multiple protected attributes, we extend our framework by incorporating two multivariate dependence measures based on distance covariance: the previously proposed joint distance covariance (JdCov) and our novel concatenated distance covariance (CCdCov), which effectively address fairness gerrymandering in both regression and classification tasks involving protected attributes of various types. We discuss and illustrate how to calibrate regularisation strength, including a method based on Jensen-Shannon divergence, which quantifies dissimilarities in prediction distributions across groups. We apply our framework to the COMPAS recidivism dataset and a large motor insurance claims dataset.

Independent component analysis (ICA) is a powerful tool for decomposing a multivariate signal or distribution into fully independent sources, not just uncorrelated ones. Unfortunately, most approaches to ICA are not robust against outliers. Here we propose a robust ICA method called RICA, which estimates the components by minimizing a robust measure of dependence between multivariate random variables. The dependence measure used is the distance correlation (dCor). In order to make it more robust we first apply a new transformation called the bowl transform, which is bounded, one-to-one, continuous, and maps far outliers to points close to the origin. This preserves the crucial property that a zero dCor implies independence. RICA estimates the independent sources sequentially, by looking for the component that has the smallest dCor with the remainder. RICA is strongly consistent and has the usual parametric rate of convergence. Its robustness is investigated by a simulation study, in which it generally outperforms its competitors. The method is illustrated on three applications, including the well-known cocktail party problem.

The main objective of fair statistical modeling and machine learning is to minimize or eliminate biases that may arise from the data or the model itself, ensuring that predictions and decisions are not unjustly influenced by sensitive attributes such as race, gender, age, or other protected characteristics. In this paper, we introduce a Fair Sufficient Representation Learning (FSRL) method that balances sufficiency and fairness. Sufficiency ensures that the representation should capture all necessary information about the target variables, while fairness requires that the learned representation remains independent of sensitive attributes. FSRL is based on a convex combination of an objective function for learning a sufficient representation and an objective function that ensures fairness. Our approach manages fairness and sufficiency at the representation level, offering a novel perspective on fair representation learning. We implement this method using distance covariance, which is effective for characterizing independence between random variables. We establish the convergence properties of the learned representations. Experiments conducted on healthcase and text datasets with diverse structures demonstrate that FSRL achieves a superior trade-off between fairness and accuracy compared to existing approaches.

Transfer learning is an important approach for addressing the challenges posed by limited data availability in various applications. It accomplishes this by transferring knowledge from well-established source domains to a less familiar target domain. However, traditional transfer learning methods often face difficulties due to rigid model assumptions and the need for a high degree of similarity between source and target domain models. In this paper, we introduce a novel method for transfer learning called Transfer learning through Enhanced Sufficient Representation (TESR). Our approach begins by estimating a sufficient and invariant representation from the source domains. This representation is then enhanced with an independent component derived from the target data, ensuring that it is sufficient for the target domain and adaptable to its specific characteristics. A notable advantage of TESR is that it does not rely on assuming similar model structures across different tasks. For example, the source domain models can be regression models, while the target domain task can be classification. This flexibility makes TESR applicable to a wide range of supervised learning problems. We explore the theoretical properties of TESR and validate its performance through simulation studies and real-world data applications, demonstrating its effectiveness in finite sample settings.

Due to the challenge posed by multi-source and heterogeneous data collected from diverse environments, causal relationships among features can exhibit variations influenced by different time spans, regions, or strategies. This diversity makes a single causal model inadequate for accurately representing complex causal relationships in all observational data, a crucial consideration in causal learning. To address this challenge, the nonlinear Causal Kernel Clustering method is introduced for heterogeneous subgroup causal learning, highlighting variations in causal relationships across diverse subgroups. The main component for clustering heterogeneous subgroups lies in the construction of the $u$-centered sample mapping function with the property of unbiased estimation, which assesses the differences in potential nonlinear causal relationships in various samples and supported by causal identifiability theory. Experimental results indicate that the method performs well in identifying heterogeneous subgroups and enhancing causal learning, leading to a reduction in prediction error.

We bridge fairness gaps from a statistical perspective by selectively utilizing either conditional distance covariance or distance covariance statistics as measures to assess the independence between predictions and sensitive attributes. We enhance fairness by incorporating sample (conditional) distance covariance as a manageable penalty term into the machine learning process. Additionally, we present the matrix form of empirical (conditional) distance covariance for parallel calculations to enhance computational efficiency. Theoretically, we provide a proof for the convergence between empirical and population (conditional) distance covariance, establishing necessary guarantees for batch computations. Through experiments conducted on a range of real-world datasets, we have demonstrated that our method effectively bridges the fairness gap in machine learning.

The paper introduces robust independence tests with non-asymptotically guaranteed significance levels for stochastic linear time-invariant systems, assuming that the observed outputs are synchronous, which means that the systems are driven by jointly i.i.d. noises. Our method provides bounds for the type I error probabilities that are distribution-free, i.e., the innovations can have arbitrary distributions. The algorithm combines confidence region estimates with permutation tests and general dependence measures, such as the Hilbert-Schmidt independence criterion and the distance covariance, to detect any nonlinear dependence between the observed systems. We also prove the consistency of our hypothesis tests under mild assumptions and demonstrate the ideas through the example of autoregressive systems.

Accurate and efficient detection of ovarian cancer at early stages is critical to ensure proper treatments for patients. Among the first-line modalities investigated in studies of early diagnosis are features distilled from protein mass spectra. This method, however, considers only a specific subset of spectral responses and ignores the interplay among protein expression levels, which can also contain diagnostic information. We propose a new modality that automatically searches protein mass spectra for discriminatory features by considering the self-similar nature of the spectra. Self-similarity is assessed by taking a wavelet decomposition of protein mass spectra and estimating the rate of level-wise decay in the energies of the resulting wavelet coefficients. Level-wise energies are estimated in a robust manner using distance variance, and rates are estimated locally via a rolling window approach. This results in a collection of rates that can be used to characterize the interplay among proteins, which can be indicative of cancer presence. Discriminatory descriptors are then selected from these evolutionary rates and used as classifying features. The proposed wavelet-based features are used in conjunction with features proposed in the existing literature for early stage diagnosis of ovarian cancer using two datasets published by the American National Cancer Institute. Including the wavelet-based features from the new modality results in improvements in diagnostic performance for early-stage ovarian cancer detection. This demonstrates the ability of the proposed modality to characterize new ovarian cancer diagnostic information.