We present a novel quantum high-dimensional linear regression algorithm with an $\ell_1$-penalty based on the classical LARS (Least Angle Regression) pathwise algorithm. Similarly to available classical numerical algorithms for Lasso, our quantum algorithm provides the full regularisation path as the penalty term varies, but quadratically faster per iteration under specific conditions. A quadratic speedup on the number of features/predictors $d$ is possible by using the simple quantum minimum-finding subroutine from D\"urr and Hoyer (arXiv'96) in order to obtain the joining time at each iteration. We then improve upon this simple quantum algorithm and obtain a quadratic speedup both in the number of features $d$ and the number of observations $n$ by using the recent approximate quantum minimum-finding subroutine from Chen and de Wolf (ICALP'23). As one of our main contributions, we construct a quantum unitary based on quantum amplitude estimation to approximately compute the joining times to be searched over by the approximate quantum minimum finding. Since the joining times are no longer exactly computed, it is no longer clear that the resulting approximate quantum algorithm obtains a good solution. As our second main contribution, we prove, via an approximate version of the KKT conditions and a duality gap, that the LARS algorithm (and therefore our quantum algorithm) is robust to errors. This means that it still outputs a path that minimises the Lasso cost function up to a small error if the joining times are only approximately computed. Finally, in the model where the observations are generated by an underlying linear model with an unknown coefficient vector, we prove bounds on the difference between the unknown coefficient vector and the approximate Lasso solution, which generalises known results about convergence rates in classical statistical learning theory analysis.

This study investigates the misclassification excess risk bound in the context of 1-bit matrix completion, a significant problem in machine learning involving the recovery of an unknown matrix from a limited subset of its entries. Matrix completion has garnered considerable attention in the last two decades due to its diverse applications across various fields. Unlike conventional approaches that deal with real-valued samples, 1-bit matrix completion is concerned with binary observations. While prior research has predominantly focused on the estimation error of proposed estimators, our study shifts attention to the prediction error. This paper offers theoretical analysis regarding the prediction errors of two previous works utilizing the logistic regression model: one employing a max-norm constrained minimization and the other employing nuclear-norm penalization. Significantly, our findings demonstrate that the latter achieves the minimax-optimal rate without the need for an additional logarithmic term. These novel results contribute to a deeper understanding of 1-bit matrix completion by shedding light on the predictive performance of specific methodologies.

Development of comprehensive prediction models are often of great interest in many disciplines of science, but datasets with information on all desired features typically have small sample sizes. In this article, we describe a transfer learning approach for building high-dimensional generalized linear models using data from a main study that has detailed information on all predictors, and from one or more external studies that have ascertained a more limited set of predictors. We propose using the external dataset(s) to build reduced model(s) and then transfer the information on underlying parameters for the analysis of the main study through a set of calibration equations, while accounting for the study-specific effects of certain design variables. We then use a generalized method of moment (GMM) with penalization for parameter estimation and develop highly scalable algorithms for fitting models taking advantage of the popular glmnet package. We further show that the use of adaptive-Lasso penalty leads to the oracle property of underlying parameter estimates and thus leads to convenient post-selection inference procedures. We conduct extensive simulation studies to investigate both predictive performance and post-selection inference properties of the proposed method. Finally, we illustrate a timely application of the proposed method for the development of risk prediction models for five common diseases using the UK Biobank study, combining baseline information from all study participants (500K) and recently released high-throughout proteomic data (# protein = 1500) on a subset (50K) of the participants.

Estimation of heterogeneous treatment effects (HTE) is of prime importance in many disciplines, ranging from personalized medicine to economics among many others. Random forests have been shown to be a flexible and powerful approach to HTE estimation in both randomized trials and observational studies. In particular "causal forests", introduced by Athey, Tibshirani and Wager (2019), along with the R implementation in package grf were rapidly adopted. A related approach, called "model-based forests", that is geared towards randomized trials and simultaneously captures effects of both prognostic and predictive variables, was introduced by Seibold, Zeileis and Hothorn (2018) along with a modular implementation in the R package model4you. Here, we present a unifying view that goes beyond the theoretical motivations and investigates which computational elements make causal forests so successful and how these can be blended with the strengths of model-based forests. To do so, we show that both methods can be understood in terms of the same parameters and model assumptions for an additive model under L2 loss. This theoretical insight allows us to implement several flavors of "model-based causal forests" and dissect their different elements in silico. The original causal forests and model-based forests are compared with the new blended versions in a benchmark study exploring both randomized trials and observational settings. In the randomized setting, both approaches performed akin. If confounding was present in the data generating process, we found local centering of the treatment indicator with the corresponding propensities to be the main driver for good performance. Local centering of the outcome was less important, and might be replaced or enhanced by simultaneous split selection with respect to both prognostic and predictive effects.

Kernel Adaptive Filtering (KAF) are mathematically principled methods which search for a function in a Reproducing Kernel Hilbert Space. While they work well for tasks such as time series prediction and system identification they are plagued by a linear relationship between number of training samples and model size, hampering their use on the very large data sets common in today's data saturated world. Previous methods try to solve this issue by sparsification. We describe a novel view of optimal filtering which may provide a route towards solutions in a RKHS which do not necessarily have this linear growth in model size. We do this by defining a RKHS in which the time structure of a stochastic process is still present. Using correntropy [11], an extension of the idea of a covariance function, we create a time based functional which describes some potentially nonlinear desired mapping function. This form of a solution may provide a fruitful line of research for creating more efficient representations of functionals in a RKHS, while theoretically providing computational complexity in the test set similar to Wiener solution.

Machine Learning (ML) algorithms are powerful data-driven tools for approximating highdimensional or non-linear nuisance functions which are useful in practice because the true functional form of the predictors is ex-ante unknown. In this paper, we develop estimators of policy interventions from panel data which allow for non-linear effects of the confounding regressors, and investigate the performance of these estimators using three well-known ML algorithms, specifically, LASSO, classification and regression trees, and random forests. We use Double Machine Learning (DML) (Chernozhukov et al., 2018) for the estimation of causal effects of homogeneous treatments with unobserved individual heterogeneity (fixed effects) and no unobserved confounding by extending Robinson (1988)'s partially linear regression model. We develop three alternative approaches for handling unobserved individual heterogeneity based on extending the within-group estimator, first-difference estimator, and correlated random effect estimator (Mundlak, 1978) for non-linear models. Using Monte Carlo simulations, we find that conventional least squares estimators can perform well even if the data generating process is nonlinear, but there are substantial performance gains in terms of bias reduction under a process where the true effect of the regressors is non-linear and discontinuous. However, for the same scenarios, we also find - despite extensive hyperparameter tuning - inference to be problematic for both tree-based learners because these lead to highly non-normal estimator distributions and the estimator variance being severely under-estimated. This contradicts the performance of trees in other circumstances and requires further investigation. Finally, we provide an illustrative example of DML for observational panel data showing the impact of the introduction of the national minimum wage in the UK.

Data valuation has wide use cases in machine learning, including improving data quality and creating economic incentives for data sharing. This paper studies the robustness of data valuation to noisy model performance scores. Particularly, we find that the inherent randomness of the widely used stochastic gradient descent can cause existing data value notions (e.g., the Shapley value and the Leave-one-out error) to produce inconsistent data value rankings across different runs. To address this challenge, we introduce the concept of safety margin, which measures the robustness of a data value notion. We show that the Banzhaf value, a famous value notion that originated from cooperative game theory literature, achieves the largest safety margin among all semivalues (a class of value notions that satisfy crucial properties entailed by ML applications and include the famous Shapley value and Leave-one-out error). We propose an algorithm to efficiently estimate the Banzhaf value based on the Maximum Sample Reuse (MSR) principle. Our evaluation demonstrates that the Banzhaf value outperforms the existing semivalue-based data value notions on several ML tasks such as learning with weighted samples and noisy label detection. Overall, our study suggests that when the underlying ML algorithm is stochastic, the Banzhaf value is a promising alternative to the other semivalue-based data value schemes given its computational advantage and ability to robustly differentiate data quality.

The environmental impacts of global warming driven by methane (CH4) emissions have catalyzed significant research initiatives in developing novel technologies that enable proactive and rapid detection of CH4. Several data-driven machine learning (ML) models were tested to determine how well they identified fugitive CH4 and its related intensity in the affected areas. Various meteorological characteristics, including wind speed, temperature, pressure, relative humidity, water vapor, and heat flux, were included in the simulation. We used the ensemble learning method to determine the best-performing weighted ensemble ML models built upon several weaker lower-layer ML models to (i) detect the presence of CH4 as a classification problem and (ii) predict the intensity of CH4 as a regression problem.

To understand how well a large language model captures certain semantic or syntactic features, researchers typically apply probing classifiers. However, the accuracy of these classifiers is critical for the correct interpretation of the results. If a probing classifier exhibits low accuracy, this may be due either to the fact that the language model does not capture the property under investigation, or to shortcomings in the classifier itself, which is unable to adequately capture the characteristics encoded in the internal representations of the model. Consequently, for more effective diagnosis, it is necessary to use the most accurate classifiers possible for a particular type of task. Logistic regression on the output representation of the transformer neural network layer is most often used to probing the syntactic properties of the language model. We show that using gradient boosting decision trees at the Knowledge Neuron layer, i.e., at the hidden layer of the feed-forward network of the transformer as a probing classifier for recognizing parts of a sentence is more advantageous than using logistic regression on the output representations of the transformer layer. This approach is also preferable to many other methods. The gain in error rate, depending on the preset, ranges from 9-54%

Fairness in decision-making has been a long-standing issue in our society. Compared to algorithmic fairness, fairness in human decisions is even more important since there are processes where humans make the final decisions and that machine learning models inherit bias from the human decisions they were trained on. However, the standard for fairness in human decisions are highly subjective and contextual. This leads to the difficulty for testing "absolute" fairness in human decisions. To bypass this issue, this work aims to test relative fairness in human decisions. That is, instead of defining what are "absolute" fair decisions, we check the relative fairness of one decision set against another. An example outcome can be: Decision Set A favors female over male more than Decision Set B. Such relative fairness has the following benefits: (1) it avoids the ambiguous and contradictory definition of "absolute" fair decisions; (2) it reveals the relative preference and bias between different human decisions; (3) if a reference set of decisions is provided, relative fairness of other decision sets against this reference set can reflect whether those decision sets are fair by the standard of that reference set. We define the relative fairness with statistical tests (null hypothesis and effect size tests) of the decision differences across each sensitive group. Furthermore, we show that a machine learning model trained on the human decisions can inherit the bias/preference and therefore can be utilized to estimate the relative fairness between two decision sets made on different data.