Testing whether a sample survey is a credible representation of the population is an important question to ensure the validity of any downstream research. While this problem, in general, does not have an efficient solution, one might take a task-based approach and aim to understand whether a certain data analysis tool, like linear regression, would yield similar answers both on the population and the sample survey. In this paper, we design an algorithm to test the credibility of a sample survey in terms of linear regression. In other words, we design an algorithm that can certify if a sample survey is good enough to guarantee the correctness of data analysis done using linear regression tools. Nowadays, one is naturally concerned about data privacy in surveys. Thus, we further test the credibility of surveys published in a differentially private manner. Specifically, we focus on Local Differential Privacy (LDP), which is a standard technique to ensure privacy in surveys where the survey participants might not trust the aggregator. We extend our algorithm to work even when the data analysis has been done using surveys with LDP. In the process, we also propose an algorithm that learns with high probability the guarantees a linear regression model on a survey published with LDP. Our algorithm also serves as a mechanism to learn linear regression models from data corrupted with noise coming from any subexponential distribution. We prove that it achieves the optimal estimation error bound for $\ell_1$ linear regression, which might be of broader interest. We prove the theoretical correctness of our algorithms while trying to reduce the sample complexity for both public and private surveys. We also numerically demonstrate the performance of our algorithms on real and synthetic datasets.

Temporal missingness, defined as unobserved patterns in time series, and its predictive potentials represent an emerging area in clinical machine learning. We trained a gated recurrent unit with decay mechanisms, called GRU-D, for a binary classification between elderly - and young patients. We extracted time series for 5 vital signs from MIMIC-IV as model inputs. GRU-D was evaluated with means of 0.780 AUROC and 0.810 AUPRC on bootstrapped data. Interpreting trained model parameters, we found differences in blood pressure missingness and respiratory rate missingness as important predictors learned by parameterized hidden gated units. We successfully showed how GRU-D can be used to reveal patterns in temporal missingness building the basis of novel research directions.

Uncertainty quantification is crucial to account for the imperfect predictions of machine learning algorithms for high-impact applications. Conformal prediction (CP) is a powerful framework for uncertainty quantification that generates calibrated prediction intervals with valid coverage. In this work, we study how CP intervals are affected by bias - the systematic deviation of a prediction from ground truth values - a phenomenon prevalent in many real-world applications. We investigate the influence of bias on interval lengths of two different types of adjustments -- symmetric adjustments, the conventional method where both sides of the interval are adjusted equally, and asymmetric adjustments, a more flexible method where the interval can be adjusted unequally in positive or negative directions. We present theoretical and empirical analyses characterizing how symmetric and asymmetric adjustments impact the "tightness" of CP intervals for regression tasks. Specifically for absolute residual and quantile-based non-conformity scores, we prove: 1) the upper bound of symmetrically adjusted interval lengths increases by $2|b|$ where $b$ is a globally applied scalar value representing bias, 2) asymmetrically adjusted interval lengths are not affected by bias, and 3) conditions when asymmetrically adjusted interval lengths are guaranteed to be smaller than symmetric ones. Our analyses suggest that even if predictions exhibit significant drift from ground truth values, asymmetrically adjusted intervals are still able to maintain the same tightness and validity of intervals as if the drift had never happened, while symmetric ones significantly inflate the lengths. We demonstrate our theoretical results with two real-world prediction tasks: sparse-view computed tomography (CT) reconstruction and time-series weather forecasting. Our work paves the way for more bias-robust machine learning systems.

When making treatment selection decisions, it is essential to include a causal effect estimation analysis to compare potential outcomes under different treatments or controls, assisting in optimal selection. However, merely estimating individual treatment effects may not suffice for truly optimal decisions. Our study addressed this issue by incorporating additional criteria, such as the estimations' uncertainty, measured by the conditional value-at-risk, commonly used in portfolio and insurance management. For continuous outcomes observable before and after treatment, we incorporated a specific prediction condition. We prioritized treatments that could yield optimal treatment effect results and lead to post-treatment outcomes more desirable than pretreatment levels, with the latter condition being called the prediction criterion. With these considerations, we propose a comprehensive methodology for multitreatment selection. Our approach ensures satisfaction of the overlap assumption, crucial for comparing outcomes for treated and control groups, by training propensity score models as a preliminary step before employing traditional causal models. To illustrate a practical application of our methodology, we applied it to the credit card limit adjustment problem. Analyzing a fintech company's historical data, we found that relying solely on counterfactual predictions was inadequate for appropriate credit line modifications. Incorporating our proposed additional criteria significantly enhanced policy performance.

We address the problem of solving strongly convex and smooth minimization problems using stochastic gradient descent (SGD) algorithm with a constant step size. Previous works suggested to combine the Polyak-Ruppert averaging procedure with the Richardson-Romberg extrapolation technique to reduce the asymptotic bias of SGD at the expense of a mild increase of the variance. We significantly extend previous results by providing an expansion of the mean-squared error of the resulting estimator with respect to the number of iterations $n$. More precisely, we show that the mean-squared error can be decomposed into the sum of two terms: a leading one of order $\mathcal{O}(n^{-1/2})$ with explicit dependence on a minimax-optimal asymptotic covariance matrix, and a second-order term of order $\mathcal{O}(n^{-3/4})$ where the power $3/4$ can not be improved in general. We also extend this result to the $p$-th moment bound keeping optimal scaling of the remainders with respect to $n$. Our analysis relies on the properties of the SGD iterates viewed as a time-homogeneous Markov chain. In particular, we establish that this chain is geometrically ergodic with respect to a suitably defined weighted Wasserstein semimetric.

We introduce a new framework for dimension reduction in the context of high-dimensional regression. Our proposal is to aggregate an ensemble of random projections, which have been carefully chosen based on the empirical regression performance after being applied to the covariates. More precisely, we consider disjoint groups of independent random projections, apply a base regression method after each projection, and retain the projection in each group based on the empirical performance. We aggregate the selected projections by taking the singular value decomposition of their empirical average and then output the leading order singular vectors. A particularly appealing aspect of our approach is that the singular values provide a measure of the relative importance of the corresponding projection directions, which can be used to select the final projection dimension. We investigate in detail (and provide default recommendations for) various aspects of our general framework, including the projection distribution and the base regression method, as well as the number of random projections used. Additionally, we investigate the possibility of further reducing the dimension by applying our algorithm twice in cases where projection dimension recommended in the initial application is too large. Our theoretical results show that the error of our algorithm stabilises as the number of groups of projections increases. We demonstrate the excellent empirical performance of our proposal in a large numerical study using simulated and real data.

Among the many possible interpolators that a deep neural network (DNN) can find, Papyan et al. (2020) showed a strong bias of gradient-based training towards representations with a highly symmetric structure in the penultimate layer, which was dubbed neural collapse (NC). In particular, the feature vectors of the training data in the penultimate layer collapse to a single vector per class (NC1); these vectors form orthogonal or simplex equiangular tight frames (NC2), and they are aligned with the last layer's row weight vectors (NC3). The question of why and how neural collapse emerges has been considered by a popular line of research, see e.g. Lu & Steinerberger (2022); E & Wojtowytsch (2022) and the discussion in Section 2. Many of these works focus on a simplified mathematical framework: the unconstrained features model (UFM) (Mixon et al., 2020; Han et al., 2022; Zhou et al., 2022a), corresponding to the joint optimization over the last layer's weights and the penultimate layer's feature representations, which are treated as free variables. To account for the existence of the training data and of all the layers before the penultimate (i.e., the backbone of the network), some form of regularization on the free features is usually added. A number of papers has proved the optimality of NC in this model (Lu & Steinerberger, 2022; E & Wojtowytsch, 2022), its emergence with gradient-based methods (Mixon et al., 2020; Han et al., 2022) and a benign loss landscape (Zhou et al., 2022a; Zhu et al., 2021). However, the major drawback of the UFM lies in its data-agnostic nature: it only acknowledges the presence of training data and backbone through a simple form of regularization (e.g., Frobenius norm or sphere constraint), which is far from being equivalent to end-to-end training.

Shapley values are a popular model-agnostic explanation framework for explaining predictions made by complex machine learning models. The framework provides feature contribution scores that sum to the predicted response and represent each feature's importance. The computation of exact Shapley values is computationally expensive due to estimating an exponential amount of non-trivial conditional expectations. The KernelSHAP framework enables us to approximate the Shapley values using a sampled subset of weighted conditional expectations. We propose three main novel contributions: a stabilizing technique to reduce the variance of the weights in the current state-of-the-art strategy, a novel weighing scheme that corrects the Shapley kernel weights based on sampled subsets, and a straightforward strategy that includes the important subsets and integrates them with the corrected Shapley kernel weights. We compare these new approximation strategies against existing ones by evaluating their Shapley value accuracy as a function of the number of subsets. The results demonstrate that our sampling strategies significantly enhance the accuracy of the approximated Shapley value explanations, making them more reliable in practical applications. This work provides valuable insights and practical recommendations for researchers and practitioners seeking to implement Shapley value-based explainability of their models.

The Adam optimizer is widely used for transformer optimization in practice, which makes understanding the underlying optimization mechanisms an important problem. However, due to the Adam's complexity, theoretical analysis of how it optimizes transformers remains a challenging task. Fortunately, Sign Gradient Descent (SignGD) serves as an effective surrogate for Adam. Despite its simplicity, theoretical understanding of how SignGD optimizes transformers still lags behind. In this work, we study how SignGD optimizes a two-layer transformer -- consisting of a softmax attention layer with trainable query-key parameterization followed by a linear layer -- on a linearly separable noisy dataset. We identify four stages in the training dynamics, each exhibiting intriguing behaviors. Based on the training dynamics, we prove the fast convergence but poor generalization of the learned transformer on the noisy dataset. We also show that Adam behaves similarly to SignGD in terms of both optimization and generalization in this setting. Additionally, we find that the poor generalization of SignGD is not solely due to data noise, suggesting that both SignGD and Adam requires high-quality data for real-world tasks. Finally, experiments on synthetic and real-world datasets empirically support our theoretical results.

RF-GAP has recently been introduced as an improved random forest proximity measure. In this paper, we present PF-GAP, an extension of RF-GAP proximities to proximity forests, an accurate and efficient time series classification model. We use the forest proximities in connection with Multi-Dimensional Scaling to obtain vector embeddings of univariate time series, comparing the embeddings to those obtained using various time series distance measures. We also use the forest proximities alongside Local Outlier Factors to investigate the connection between misclassified points and outliers, comparing with nearest neighbor classifiers which use time series distance measures. We show that the forest proximities may exhibit a stronger connection between misclassified points and outliers than nearest neighbor classifiers.