Multi-calibration is a powerful and evolving concept originating in the field of algorithmic fairness. For a predictor $f$ that estimates the outcome $y$ given covariates $x$, and for a function class $\mathcal{C}$, multi-calibration requires that the predictor $f(x)$ and outcome $y$ are indistinguishable under the class of auditors in $\mathcal{C}$. Fairness is captured by incorporating demographic subgroups into the class of functions~$\mathcal{C}$. Recent work has shown that, by enriching the class $\mathcal{C}$ to incorporate appropriate propensity re-weighting functions, multi-calibration also yields target-independent learning, wherein a model trained on a source domain performs well on unseen, future, target domains(approximately) captured by the re-weightings. Formally, multi-calibration with respect to $\mathcal{C}$ bounds $\big|\mathbb{E}_{(x,y)\sim \mathcal{D}}[c(f(x),x)\cdot(f(x)-y)]\big|$ for all $c \in \mathcal{C}$. In this work, we view the term $(f(x)-y)$ as just one specific mapping, and explore the power of an enriched class of mappings. We propose \textit{HappyMap}, a generalization of multi-calibration, which yields a wide range of new applications, including a new fairness notion for uncertainty quantification (conformal prediction), a novel technique for conformal prediction under covariate shift, and a different approach to analyzing missing data, while also yielding a unified understanding of several existing seemingly disparate algorithmic fairness notions and target-independent learning approaches. We give a single \textit{HappyMap} meta-algorithm that captures all these results, together with a sufficiency condition for its success.

This paper addresses the problem of set-to-set matching, which involves matching two different sets of items based on some criteria, especially in the case of high-dimensional items like images. Although neural networks have been applied to solve this problem, most machine learning-based approaches assume that the training and test data follow the same distribution, which is not always true in real-world scenarios. To address this limitation, we introduce SHIFT15M, a dataset that can be used to evaluate set-to-set matching models when the distribution of data changes between training and testing. We conduct benchmark experiments that demonstrate the performance drop of naive methods due to distribution shift. Additionally, we provide software to handle the SHIFT15M dataset in a simple manner, with the URL for the software to be made available after publication of this manuscript. We believe proposed SHIFT15M dataset provide a valuable resource for evaluating set-to-set matching models under the distribution shift.

Bayesian Causal Forests (BCF) is a causal inference machine learning model based on a highly flexible non-parametric regression and classification tool called Bayesian Additive Regression Trees (BART). Motivated by data from the Trends in International Mathematics and Science Study (TIMSS), which includes data on student achievement in both mathematics and science, we present a multivariate extension of the BCF algorithm. With the help of simulation studies we show that our approach can accurately estimate causal effects for multiple outcomes subject to the same treatment. We also apply our model to Irish data from TIMSS 2019. Our findings reveal the positive effects of having access to a study desk at home (Mathematics ATE 95% CI: [0.20, 11.67]) while also highlighting the negative consequences of students often feeling hungry at school (Mathematics ATE 95% CI: [-11.15, -2.78] , Science ATE 95% CI: [-10.82,-1.72]) or often being absent (Mathematics ATE 95% CI: [-12.47, -1.55]).

While quantum machine learning (ML) has been proposed to be one of the most promising applications of quantum computing, how to build quantum ML models that outperform classical ML remains a major open question. Here, we demonstrate a Bayesian algorithm for constructing quantum kernels for support vector machines that adapts quantum gate sequences to data. The algorithm increases the complexity of quantum circuits incrementally by appending quantum gates selected with Bayesian information criterion as circuit selection metric and Bayesian optimization of the parameters of the locally optimal quantum circuits identified. The goal is to build quantum kernels for SVM that can solve classification problems with as little training data as possible. The performance of the resulting quantum models for the classification problems considered here significantly exceeds that of optimized classical models with conventional kernels.

Questions on class cardinality comparisons are quite tricky to answer and come with its own challenges. They require some kind of reasoning since web documents and knowledge bases, indispensable sources of information, rarely store direct answers to questions, such as, ``Are there more astronauts or Physics Nobel Laureates?'' We tackle questions on class cardinality comparison by tapping into three sources for absolute cardinalities as well as the cardinalities of orthogonal subgroups of the classes. We propose novel techniques for aggregating signals with partial coverage for more reliable estimates and evaluate them on a dataset of 4005 class pairs, achieving an accuracy of 83.7%.

In clinical practice, many diagnosis tasks rely on the identification of cells in histopathology images. While supervised machine learning techniques require labels, providing manual cell annotations is time-consuming due to the large number of cells. In this paper, we propose a self-supervised framework (VOLTA) for cell representation learning in histopathology images using a novel technique that accounts for the cell's mutual relationship with its environment for improved cell representations. We subjected our model to extensive experiments on the data collected from multiple institutions around the world comprising of over 700,000 cells, four cancer types, and cell types ranging from three to six categories for each dataset. The results show that our model outperforms the state-of-the-art models in cell representation learning. To showcase the potential power of our proposed framework, we applied VOLTA to ovarian and endometrial cancers with very small sample sizes (10-20 samples) and demonstrated that our cell representations can be utilized to identify the known histotypes of ovarian cancer and provide novel insights that link histopathology and molecular subtypes of endometrial cancer. Unlike supervised deep learning models that require large sample sizes for training, we provide a framework that can empower new discoveries without any annotation data in situations where sample sizes are limited.

This paper introduces a novel algorithm, the Perturbed Proximal Preconditioned SPIDER algorithm (3P-SPIDER), designed to solve finite sum non-convex composite optimization. It is a stochastic Variable Metric Forward-Backward algorithm, which allows approximate preconditioned forward operator and uses a variable metric proximity operator as the backward operator; it also proposes a mini-batch strategy with variance reduction to address the finite sum setting. We show that 3P-SPIDER extends some Stochastic preconditioned Gradient Descent-based algorithms and some Incremental Expectation Maximization algorithms to composite optimization and to the case the forward operator can not be computed in closed form. We also provide an explicit control of convergence in expectation of 3P-SPIDER, and study its complexity in order to satisfy the epsilon-approximate stationary condition. Our results are the first to combine the composite non-convex optimization setting, a variance reduction technique to tackle the finite sum setting by using a minibatch strategy and, to allow deterministic or random approximations of the preconditioned forward operator. Finally, through an application to inference in a logistic regression model with random effects, we numerically compare 3P-SPIDER to other stochastic forward-backward algorithms and discuss the role of some design parameters of 3P-SPIDER.

Byzantine-robustness has been gaining a lot of attention due to the growth of the interest in collaborative and federated learning. However, many fruitful directions, such as the usage of variance reduction for achieving robustness and communication compression for reducing communication costs, remain weakly explored in the field. This work addresses this gap and proposes Byz-VR-MARINA - a new Byzantine-tolerant method with variance reduction and compression. A key message of our paper is that variance reduction is key to fighting Byzantine workers more effectively. At the same time, communication compression is a bonus that makes the process more communication efficient. We derive theoretical convergence guarantees for Byz-VR-MARINA outperforming previous state-of-the-art for general non-convex and Polyak-Lojasiewicz loss functions. Unlike the concurrent Byzantine-robust methods with variance reduction and/or compression, our complexity results are tight and do not rely on restrictive assumptions such as boundedness of the gradients or limited compression. Moreover, we provide the first analysis of a Byzantine-tolerant method supporting non-uniform sampling of stochastic gradients. Numerical experiments corroborate our theoretical findings.

In many longitudinal settings, time-varying covariates may not be measured at the same time as responses and are often prone to measurement error. Naive last-observation-carried-forward methods incur estimation biases, and existing kernel-based methods suffer from slow convergence rates and large variations. To address these challenges, we propose a new functional calibration approach to efficiently learn longitudinal covariate processes based on sparse functional data with measurement error. Our approach, stemming from functional principal component analysis, calibrates the unobserved synchronized covariate values from the observed asynchronous and error-prone covariate values, and is broadly applicable to asynchronous longitudinal regression with time-invariant or time-varying coefficients. For regression with time-invariant coefficients, our estimator is asymptotically unbiased, root-n consistent, and asymptotically normal; for time-varying coefficient models, our estimator has the optimal varying coefficient model convergence rate with inflated asymptotic variance from the calibration. In both cases, our estimators present asymptotic properties superior to the existing methods. The feasibility and usability of the proposed methods are verified by simulations and an application to the Study of Women's Health Across the Nation, a large-scale multi-site longitudinal study on women's health during mid-life.

For $V : \mathbb{R}^d \to \mathbb{R}$ coercive, we study the convergence rate for the $L^1$-distance of the empiric minimizer, which is the true minimum of the function $V$ sampled with noise with a finite number $n$ of samples, to the minimum of $V$. We show that in general, for unbounded functions with fast growth, the convergence rate is bounded above by $a_n n^{-1/q}$, where $q$ is the dimension of the latent random variable and where $a_n = o(n^\varepsilon)$ for every $\varepsilon > 0$. We then present applications to optimization problems arising in Machine Learning and in Monte Carlo simulation.