Confounding is a significant obstacle to unbiased estimation of causal effects from observational data. For settings with high-dimensional covariates -- such as text data, genomics, or the behavioral social sciences -- researchers have proposed methods to adjust for confounding by adapting machine learning methods to the goal of causal estimation. However, empirical evaluation of these adjustment methods has been challenging and limited. In this work, we build on a promising empirical evaluation strategy that simplifies evaluation design and uses real data: subsampling randomized controlled trials (RCTs) to create confounded observational datasets while using the average causal effects from the RCTs as ground-truth. We contribute a new sampling algorithm, which we call RCT rejection sampling, and provide theoretical guarantees that causal identification holds in the observational data to allow for valid comparisons to the ground-truth RCT. Using synthetic data, we show our algorithm indeed results in low bias when oracle estimators are evaluated on the confounded samples, which is not always the case for a previously proposed algorithm. In addition to this identification result, we highlight several finite data considerations for evaluation designers who plan to use RCT rejection sampling on their own datasets. As a proof of concept, we implement an example evaluation pipeline and walk through these finite data considerations with a novel, real-world RCT -- which we release publicly -- consisting of approximately 70k observations and text data as high-dimensional covariates. Together, these contributions build towards a broader agenda of improved empirical evaluation for causal estimation.

With the development and popularity of sensors installed in manufacturing systems, complex data are collected during manufacturing processes, which brings challenges for traditional process control methods. This paper proposes a novel process control and monitoring method for the complex structure of high-dimensional image-based overlay errors (modeled in tensor form), which are collected in semiconductor manufacturing processes. The proposed method aims to reduce overlay errors using limited control recipes. We first build a high-dimensional process model and propose different tensor-on-vector regression algorithms to estimate parameters in the model to alleviate the curse of dimensionality. Then, based on the estimate of tensor parameters, the exponentially weighted moving average (EWMA) controller for tensor data is designed whose stability is theoretically guaranteed. Considering the fact that low-dimensional control recipes cannot compensate for all high-dimensional disturbances on the image, control residuals are monitored to prevent significant drifts of uncontrollable high-dimensional disturbances. Through extensive simulations and real case studies, the performances of parameter estimation algorithms and the EWMA controller in tensor space are evaluated. Compared with existing image-based feedback controllers, the superiority of our method is verified especially when disturbances are not stable.

We present a theoretical analysis of the performance of transformer with softmax attention in in-context learning with linear regression tasks. While the existing literature predominantly focuses on the convergence of transformers with single-/multi-head attention, our research centers on comparing their performance. We conduct an exact theoretical analysis to demonstrate that multi-head attention with a substantial embedding dimension performs better than single-head attention. When the number of in-context examples D increases, the prediction loss using single- /multi-head attention is in O (1 /D), and the one for multi-head attention has a smaller multiplicative constant. In addition to the simplest data distribution setting, we consider more scenarios, e.g., noisy labels, local examples, correlated features, and prior knowledge. We observe that, in general, multi-head attention is preferred over single-head attention. Our results verify the effectiveness of the design of multi-head attention in the transformer architecture.

The increased application of machine learning (ML) in sensitive domains requires protecting the training data through privacy frameworks, such as differential privacy (DP). DP requires to specify a uniform privacy level $\varepsilon$ that expresses the maximum privacy loss that each data point in the entire dataset is willing to tolerate. Yet, in practice, different data points often have different privacy requirements. Having to set one uniform privacy level is usually too restrictive, often forcing a learner to guarantee the stringent privacy requirement, at a large cost to accuracy. To overcome this limitation, we introduce our novel Personalized-DP Output Perturbation method (PDP-OP) that enables to train Ridge regression models with individual per data point privacy levels. We provide rigorous privacy proofs for our PDP-OP as well as accuracy guarantees for the resulting model. This work is the first to provide such theoretical accuracy guarantees when it comes to personalized DP in machine learning, whereas previous work only provided empirical evaluations. We empirically evaluate PDP-OP on synthetic and real datasets and with diverse privacy distributions. We show that by enabling each data point to specify their own privacy requirement, we can significantly improve the privacy-accuracy trade-offs in DP. We also show that PDP-OP outperforms the personalized privacy techniques of Jorgensen et al. (2015).

We developed an artificial intelligence approach to predict the transfer fee of a football player. This model can help clubs make better decisions about which players to buy and sell, which can lead to improved performance and increased club budgets. Having collected data on player performance, transfer fees, and other factors that might affect a player's value, we then used this data to train a machine learning model that can accurately predict a player's impact on the game. We further passed the obtained results as one of the features to the predictor of transfer fees. The model can help clubs identify players who are undervalued and who could be sold for a profit. It can also help clubs avoid overpaying for players. We believe that our model can be a valuable tool for football clubs. It can help them make better decisions about player recruitment and transfers.

Training machine learning and statistical models often involves optimizing a data-driven risk criterion. The risk is usually computed with respect to the empirical data distribution, but this may result in poor and unstable out-of-sample performance due to distributional uncertainty. In the spirit of distributionally robust optimization, we propose a novel robust criterion by combining insights from Bayesian nonparametric (i.e., Dirichlet Process) theory and recent decision-theoretic models of smooth ambiguity-averse preferences. First, we highlight novel connections with standard regularized empirical risk minimization techniques, among which Ridge and LASSO regressions. Then, we theoretically demonstrate the existence of favorable finite-sample and asymptotic statistical guarantees on the performance of the robust optimization procedure. For practical implementation, we propose and study tractable approximations of the criterion based on well-known Dirichlet Process representations. We also show that the smoothness of the criterion naturally leads to standard gradient-based numerical optimization. Finally, we provide insights into the workings of our method by applying it to high-dimensional sparse linear regression and robust location parameter estimation tasks.

Online Judge (OJ) systems are typically considered within programming-related courses as they yield fast and objective assessments of the code developed by the students. Such an evaluation generally provides a single decision based on a rubric, most commonly whether the submission successfully accomplished the assignment. Nevertheless, since in an educational context such information may be deemed insufficient, it would be beneficial for both the student and the instructor to receive additional feedback about the overall development of the task. This work aims to tackle this limitation by considering the further exploitation of the information gathered by the OJ and automatically inferring feedback for both the student and the instructor. More precisely, we consider the use of learning-based schemes -- particularly, multi-instance learning (MIL) and classical machine learning formulations -- to model student behavior. Besides, explainable artificial intelligence (XAI) is contemplated to provide human-understandable feedback. The proposal has been evaluated considering a case of study comprising 2500 submissions from roughly 90 different students from a programming-related course in a computer science degree. The results obtained validate the proposal: The model is capable of significantly predicting the user outcome (either passing or failing the assignment) solely based on the behavioral pattern inferred by the submissions provided to the OJ. Moreover, the proposal is able to identify prone-to-fail student groups and profiles as well as other relevant information, which eventually serves as feedback to both the student and the instructor.

We present an approach to outsourcing of training neural networks while preserving data confidentiality from malicious parties. We use fully homomorphic encryption to build a unified training approach that works on encrypted data and learns quantized neural network models. The data can be horizontally or vertically split between multiple parties, enabling collaboration on confidential data. We train logistic regression and multi-layer perceptrons on several datasets.

Sign-Perturbed Sum (SPS) is a powerful finite-sample system identification algorithm which can construct confidence regions for the true data generating system with exact coverage probabilities, for any finite sample size. SPS was developed in a series of papers and it has a wide range of applications, from general linear systems, even in a closed-loop setup, to nonlinear and nonparametric approaches. Although several theoretical properties of SPS were proven in the literature, the sample complexity of the method was not analysed so far. This paper aims to fill this gap and provides the first results on the sample complexity of SPS. Here, we focus on scalar linear regression problems, that is we study the behaviour of SPS confidence intervals. We provide high probability upper bounds, under three different sets of assumptions, showing that the sizes of SPS confidence intervals shrink at a geometric rate around the true parameter, if the observation noises are subgaussian. We also show that similar bounds hold for the previously proposed outer approximation of the confidence region. Finally, we present simulation experiments comparing the theoretical and the empirical convergence rates.

Logistic regression is a ubiquitous method for probabilistic classification. However, the effectiveness of logistic regression depends upon careful and relatively computationally expensive tuning, especially for the regularisation hyperparameter, and especially in the context of high-dimensional data. We present a prevalidated ridge regression model that closely matches logistic regression in terms of classification error and log-loss, particularly for high-dimensional data, while being significantly more computationally efficient and having effectively no hyperparameters beyond regularisation. We scale the coefficients of the model so as to minimise log-loss for a set of prevalidated predictions derived from the estimated leave-one-out cross-validation error. This exploits quantities already computed in the course of fitting the ridge regression model in order to find the scaling parameter with nominal additional computational expense.