Kernel methods are a cornerstone of classical machine learning. The idea of using quantum computers to compute kernels has recently attracted attention. Quantum embedding kernels (QEKs) constructed by embedding data into the Hilbert space of a quantum computer are a particular quantum kernel technique that allows to gather insights into learning problems and that are particularly suitable for noisy intermediate-scale quantum devices. In this work, we first provide an accessible introduction to quantum embedding kernels and then analyze the practical issues arising when realizing them on a noisy near-term quantum computer. We focus on quantum embedding kernels with variational parameters. These variational parameters are optimized for a given dataset by increasing the kernel-target alignment, a heuristic connected to the achievable classification accuracy. We further show under which conditions noise from device imperfections influences the predicted kernel and provide a strategy to mitigate these detrimental effects which is tailored to quantum embedding kernels. We also address the influence of finite sampling and derive bounds that put guarantees on the quality of the kernel matrix. We illustrate our findings by numerical experiments and tests on actual hardware.

Robust estimation of a mean vector, a topic regarded as obsolete in the traditional robust statistics community, has recently surged in machine learning literature in the last decade. The latest focus is on the sub-Gaussian performance and computability of the estimators in a non-asymptotic setting. Numerous traditional robust estimators are computationally intractable, which partly contributes to the renewal of the interest in the robust mean estimation. Robust centrality estimators, however, include the trimmed mean and the sample median. The latter has the best robustness but suffers a low-efficiency drawback. Trimmed mean and median of means, %as robust alternatives to the sample mean, and achieving sub-Gaussian performance have been proposed and studied in the literature. This article investigates the robustness of leading sub-Gaussian estimators of mean and reveals that none of them can resist greater than $25\%$ contamination in data and consequently introduces an outlyingness induced winsorized mean which has the best possible robustness (can resist up to $50\%$ contamination without breakdown) meanwhile achieving high efficiency. Furthermore, it has a sub-Gaussian performance for uncontaminated samples and a bounded estimation error for contaminated samples at a given confidence level in a finite sample setting. It can be computed in linear time.

Post-deployment monitoring of the performance of ML systems is critical for ensuring reliability, especially as new user inputs can differ from the training distribution. Here we propose a novel approach, MLDemon, for ML DEployment MONitoring. MLDemon integrates both unlabeled features and a small amount of on-demand labeled examples over time to produce a real-time estimate of the ML model's current performance on a given data stream. Subject to budget constraints, MLDemon decides when to acquire additional, potentially costly, supervised labels to verify the model. On temporal datasets with diverse distribution drifts and models, MLDemon substantially outperforms existing monitoring approaches. Moreover, we provide theoretical analysis to show that MLDemon is minimax rate optimal up to logarithmic factors and is provably robust against broad distribution drifts whereas prior approaches are not.

These issues result from the fact that small part of the PIE prediction is attributed the explainers, after all, are not the decision-making process to the interaction of features via a black-box themselves. Therefore, the second area is receiving much model, with the goal to boost the predictive performance attention in recent years, that focuses on building models while maintaining interpretability. As that are inherently interpretable, such as rule-based models, such, the interpretable model captures the main decision trees, linear models, case-based models, etc., contributions of features, and the black-box model which do not need external explainers. While interpretable attempts to complement the interpretable piece by models have been advanced to achieve very competitive performance capturing the "nuances" of feature interactions compared to black-box models in some examples as a refinement. We design an iterative training by extensively searching the model space, interpretable models algorithm to jointly train the two types of models.

We develop simple methods for constructing parameter priors for model choice among Directed Acyclic Graphical (DAG) models. In particular, we introduce several assumptions that permit the construction of parameter priors for a large number of DAG models from a small set of assessments. We then present a method for directly computing the marginal likelihood of every DAG model given a random sample with no missing observations. We apply this methodology to Gaussian DAG models which consist of a recursive set of linear regression models. We show that the only parameter prior for complete Gaussian DAG models that satisfies our assumptions is the normal-Wishart distribution. Our analysis is based on the following new characterization of the Wishart distribution: let $W$ be an $n \times n$, $n \ge 3$, positive-definite symmetric matrix of random variables and $f(W)$ be a pdf of $W$. Then, f$(W)$ is a Wishart distribution if and only if $W_{11} - W_{12} W_{22}^{-1} W'_{12}$ is independent of $\{W_{12},W_{22}\}$ for every block partitioning $W_{11},W_{12}, W'_{12}, W_{22}$ of $W$. Similar characterizations of the normal and normal-Wishart distributions are provided as well.

AMP algorithms have two features that make them particularly attractive. First, they can easily be tailored to take advantage of prior information on the structure of the signal, such as sparsity or other constraints. Second, under suitable assumptions on a design or data matrix, AMP theory provides precise asymptotic guarantees for statistical procedures in the high-dimensional regime where the ratio of the number of observations n to dimensions p converges to a constant (Bayati and Montanari, 2012; Donoho et al., 2013; Sur et al., 2017). More generally, AMP has been also used to obtain lower bounds on the estimation error of first-order methods (Celentano et al., 2020), and in linear regression and low rank matrix estimation, it plays a fundamental role in understanding the performance gap between information-theoretically optimal and computationally feasible estimators (Reeves and Pfister, 2019; Barbier et al., 2019; Lelarge and Miolane, 2019). In these settings, it is conjectured that AMP achieves the optimal asymptotic estimation error among all polynomial-time algorithms (cf.

Patient monitoring is vital in all stages of care. We here report the development and validation of ICU length of stay and mortality prediction models. The models will be used in an intelligent ICU patient monitoring module of an Intelligent Remote Patient Monitoring (IRPM) framework that monitors the health status of patients, and generates timely alerts, maneuver guidance, or reports when adverse medical conditions are predicted. We utilized the publicly available Medical Information Mart for Intensive Care (MIMIC) database to extract ICU stay data for adult patients to build two prediction models: one for mortality prediction and another for ICU length of stay. For the mortality model, we applied six commonly used machine learning (ML) binary classification algorithms for predicting the discharge status (survived or not). For the length of stay model, we applied the same six ML algorithms for binary classification using the median patient population ICU stay of 2.64 days. For the regression-based classification, we used two ML algorithms for predicting the number of days. We built two variations of each prediction model: one using 12 baseline demographic and vital sign features, and the other based on our proposed quantiles approach, in which we use 21 extra features engineered from the baseline vital sign features, including their modified means, standard deviations, and quantile percentages. We could perform predictive modeling with minimal features while maintaining reasonable performance using the quantiles approach. The best accuracy achieved in the mortality model was approximately 89% using the random forest algorithm. The highest accuracy achieved in the length of stay model, based on the population median ICU stay (2.64 days), was approximately 65% using the random forest algorithm.

Learning optimal policies from historical data enables the gains from personalization to be realized in a wide variety of applications. The growing policy learning literature focuses on a setting where the treatment assignment policy does not adapt to the data. However, adaptive data collection is becoming more common in practice, from two primary sources: 1) data collected from adaptive experiments that are designed to improve inferential efficiency; 2) data collected from production systems that are adaptively evolving an operational policy to improve performance over time (e.g. contextual bandits). In this paper, we aim to address the challenge of learning the optimal policy with adaptively collected data and provide one of the first theoretical inquiries into this problem. We propose an algorithm based on generalized augmented inverse propensity weighted estimators and establish its finite-sample regret bound. We complement this regret upper bound with a lower bound that characterizes the fundamental difficulty of policy learning with adaptive data. Finally, we demonstrate our algorithm's effectiveness using both synthetic data and public benchmark datasets.

Representation learning has been widely studied in the context of meta-learning, enabling rapid learning of new tasks through shared representations. Recent works such as MAML have explored using fine-tuning-based metrics, which measure the ease by which fine-tuning can achieve good performance, as proxies for obtaining representations. We present a theoretical framework for analyzing representations derived from a MAML-like algorithm, assuming the available tasks use approximately the same underlying representation. We then provide risk bounds on the best predictor found by fine-tuning via gradient descent, demonstrating that the algorithm can provably leverage the shared structure. The upper bound applies to general function classes, which we demonstrate by instantiating the guarantees of our framework in the logistic regression and neural network settings. In contrast, we establish the existence of settings where any algorithm, using a representation trained with no consideration for task-specific fine-tuning, performs as well as a learner with no access to source tasks in the worst case. This separation result underscores the benefit of fine-tuning-based methods, such as MAML, over methods with "frozen representation" objectives in few-shot learning.

This paper focuses on understanding how the generalization error scales with the amount of the training data for deep neural networks (DNNs). Existing techniques in statistical learning require computation of capacity measures, such as VC dimension, to provably bound this error. It is however unclear how to extend these measures to DNNs and therefore the existing analyses are applicable to simple neural networks, which are not used in practice, e.g., linear or shallow ones or otherwise multi-layer perceptrons. Moreover, many theoretical error bounds are not empirically verifiable. We derive estimates of the generalization error that hold for deep networks and do not rely on unattainable capacity measures. The enabling technique in our approach hinges on two major assumptions: i) the network achieves zero training error, ii) the probability of making an error on a test point is proportional to the distance between this point and its nearest training point in the feature space and at a certain maximal distance (that we call radius) it saturates. Based on these assumptions we estimate the generalization error of DNNs. The obtained estimate scales as O(1/(\delta N^{1/d})), where N is the size of the training data and is parameterized by two quantities, the effective dimensionality of the data as perceived by the network (d) and the aforementioned radius (\delta), both of which we find empirically. We show that our estimates match with the experimentally obtained behavior of the error on multiple learning tasks using benchmark data-sets and realistic models. Estimating training data requirements is essential for deployment of safety critical applications such as autonomous driving etc. Furthermore, collecting and annotating training data requires a huge amount of financial, computational and human resources. Our empirical estimates will help to efficiently allocate resources.