Modern platforms leverage randomized experiments to make informed decisions from a given set of items (``treatments''). As a particularly challenging scenario, these items may (i) arrive in high volume, with thousands of new items being released per hour, and (ii) have short lifetime, say, due to the item's transient nature or underlying non-stationarity that impels the platform to perceive the same item as distinct copies over time. Thus motivated, we study a Bayesian multiple-play bandit problem that encapsulates the key features of the multivariate testing (or ``multi-A/B testing'') problem with a high volume of short-lived arms. In each round, a set of $k$ arms arrive, each available for $w$ rounds. Without knowing the mean reward for each arm, the learner selects a multiset of $n$ arms and immediately observes their realized rewards. We aim to minimize the loss due to not knowing the mean rewards, averaged over instances generated from a given prior distribution. We show that when $k = O(n^\rho)$ for some constant $\rho>0$, our proposed policy has $\tilde O(n^{-\min \{\rho, \frac 12 (1+\frac 1w)^{-1}\}})$ loss on a sufficiently large class of prior distributions. We complement this result by showing that every policy suffers $\Omega (n^{-\min \{\rho, \frac 12\}})$ loss on the same class of distributions. We further validate the effectiveness of our policy through a large-scale field experiment on {\em Glance}, a content-card-serving platform that faces exactly the above challenge. A simple variant of our policy outperforms the platform's current recommender by 4.32\% in total duration and 7.48\% in total number of click-throughs.

In this paper we define a population parameter, ``Generalized Variable Importance Metric (GVIM)'', to measure importance of predictors for black box machine learning methods, where the importance is not represented by model-based parameter. GVIM is defined for each input variable, using the true conditional expectation function, and it measures the variable's importance in affecting a continuous or a binary response. We extend previously published results to show that the defined GVIM can be represented as a function of the Conditional Average Treatment Effect (CATE) for any kind of a predictor, which gives it a causal interpretation and further justification as an alternative to classical measures of significance that are only available in simple parametric models. Extensive set of simulations using realistically complex relationships between covariates and outcomes and number of regression techniques of varying degree of complexity show the performance of our proposed estimator of the GVIM.

This study's first purpose is to provide quantitative evidence that would incentivize researchers to instead use the more robust method of nested cross-validation. The second purpose is to present methods and MATLAB codes for doing power analysis for ML-based analysis during the design of a study. Monte Carlo simulations were used to quantify the interactions between the employed cross-validation method, the discriminative power of features, the dimensionality of the feature space, and the dimensionality of the model. Four different cross-validations (single holdout, 10-fold, train-validation-test, and nested 10-fold) were compared based on the statistical power and statistical confidence of the ML models. Distributions of the null and alternative hypotheses were used to determine the minimum required sample size for obtaining a statistically significant outcome ({\alpha}=0.05, 1-\b{eta}=0.8). Statistical confidence of the model was defined as the probability of correct features being selected and hence being included in the final model. Our analysis showed that the model generated based on the single holdout method had very low statistical power and statistical confidence and that it significantly overestimated the accuracy. Conversely, the nested 10-fold cross-validation resulted in the highest statistical confidence and the highest statistical power, while providing an unbiased estimate of the accuracy. The required sample size with a single holdout could be 50% higher than what would be needed if nested cross-validation were used. Confidence in the model based on nested cross-validation was as much as four times higher than the confidence in the single holdout-based model. A computational model, MATLAB codes, and lookup tables are provided to assist researchers with estimating the sample size during the design of their future studies.

Quantum Extreme Learning Machines (QELMs) have emerged as a promising framework for quantum machine learning. Their appeal lies in the rich feature map induced by the dynamics of a quantum substrate - the quantum reservoir - and the efficient post-measurement training via linear regression. Here we study the expressivity of QELMs by decomposing the prediction of QELMs into a Fourier series. We show that the achievable Fourier frequencies are determined by the data encoding scheme, while Fourier coefficients depend on both the reservoir and the measurement. Notably, the expressivity of QELMs is fundamentally limited by the number of Fourier frequencies and the number of observables, while the complexity of the prediction hinges on the reservoir. As a cautionary note on scalability, we identify four sources that can lead to the exponential concentration of the observables as the system size grows (randomness, hardware noise, entanglement, and global measurements) and show how this can turn QELMs into useless input-agnostic oracles. Our analysis elucidates the potential and fundamental limitations of QELMs, and lays the groundwork for systematically exploring quantum reservoir systems for other machine learning tasks.

The polyhedral method by Lee et al. (2016) introduced confidence intervals for exact selective inference in Gaussian regression models. This method provides valid inferences for selected parameters by conditioning on the outcome of selection. A pivot is obtained for each selected parameter from a truncated Gaussian distribution, provided the outcome of selection can be described by linear constraints, also known as polyhedral constraints. However, as shown by Kivaranovic and Leeb (2021), confidence intervals based on this pivot can have infinite length in expectation. Randomizing data at the time of selection and conditioning on the outcome of randomized selection produces narrower confidence intervals than the polyhedral method.

Pulmonary Hypertension (PH) is a severe disease characterized by an elevated pulmonary artery pressure. The gold standard for PH diagnosis is measurement of mean Pulmonary Artery Pressure (mPAP) during an invasive Right Heart Catheterization. In this paper, we investigate noninvasive approach to PH detection utilizing Magnetic Resonance Imaging, Computer Models and Machine Learning. We show using the ablation study, that physics-informed feature engineering based on models of blood circulation increases the performance of Gradient Boosting Decision Trees-based algorithms for classification of PH and regression of values of mPAP. We compare results of regression (with thresholding of estimated mPAP) and classification and demonstrate that metrics achieved in both experiments are comparable. The predicted mPAP values are more informative to the physicians than the probability of PH returned by classification models. They provide the intuitive explanation of the outcome of the machine learning model (clinicians are accustomed to the mPAP metric, contrary to the PH probability).

How can we build AI systems that are aligned with human values and objectives in order to avoid causing harm or violating societal standards for acceptable behavior? Making AI systems learn human-like representations of the world has many known benefits, including improving generalization, robustness to domain shifts, and few-shot learning performance, among others. We propose that this kind of representational alignment between machine learning (ML) models and humans is also a necessary condition for value alignment, where ML systems conform to human values and societal norms. We focus on ethics as one aspect of value alignment and train multiple ML agents (support vector regression and kernel regression) in a multi-armed bandit setting, where rewards are sampled from a distribution that reflects the morality of the chosen action. We then study the relationship between each agent's degree of representational alignment with humans and their performance when learning to take the most ethical actions.

Identifying optimal collective variables to model transformations, using atomic-scale simulations, is a long-standing challenge. We propose a new method for the generation, optimization, and comparison of collective variables, which can be thought of as a data-driven generalization of the path collective variable concept. It consists in a kernel ridge regression of the committor probability, which encodes a transformation's progress. The resulting collective variable is one-dimensional, interpretable, and differentiable, making it appropriate for enhanced sampling simulations requiring biasing. We demonstrate the validity of the method on two different applications: a precipitation model, and the association of Li$^+$ and F$^-$ in water. For the former, we show that global descriptors such as the permutation invariant vector allow to reach an accuracy far from the one achieved \textit{via} simpler, more intuitive variables. For the latter, we show that information correlated with the transformation mechanism is contained in the first solvation shell only, and that inertial effects prevent the derivation of optimal collective variables from the atomic positions only.

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.