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We study the problem of estimating a rank-$1$ signal in the presence of rotationally invariant noise-a class of perturbations more general than Gaussian noise. Principal Component Analysis (PCA) provides a natural estimator, and sharp results on its performance have been obtained in the high-dimensional regime. Recently, an Approximate Message Passing (AMP) algorithm has been proposed as an alternative estimator with the potential to improve the accuracy of PCA. However, the existing analysis of AMP requires an initialization that is both correlated with the signal and independent of the noise, which is often unrealistic in practice. In this work, we combine the two methods, and propose to initialize AMP with PCA. Our main result is a rigorous asymptotic characterization of the performance of this estimator. Both the AMP algorithm and its analysis differ from those previously derived in the Gaussian setting: at every iteration, our AMP algorithm requires a specific term to account for PCA initialization, while in the Gaussian case, PCA initialization affects only the first iteration of AMP. The proof is based on a two-phase artificial AMP that first approximates the PCA estimator and then mimics the true AMP. Our numerical simulations show an excellent agreement between AMP results and theoretical predictions, and suggest an interesting open direction on achieving Bayes-optimal performance.

Data mining techniques offer great opportunities for developing ethics lines, tools for communication, participation and innovation whose main aim is to ensure improvements and compliance with the values, conduct and commitments making up the code of ethics. The aim of this study is to suggest a process for exploiting the data generated by the data generated and collected from an ethics line by extracting rules of association and applying the Apriori algorithm. This makes it possible to identify anomalies and behaviour patterns requiring action to review, correct, promote or expand them, as appropriate. Finally, I offer a simulated application of the Apriori algorithm, supplying it with synthetic data to find out its potential, strengths and limitations.

Along with confounding, selection bias is one of the fundamental threats to the validity of epidemiologic research. Unlike confounding, it has yet to be given a standard definition in terms of potential outcomes. Traditionally, selection bias has been defined as a systematic difference in a measure of the exposure-disease association in the study population and the population eligible for inclusion. This definition depends on the parameterization of the association between exposure and disease. The structural approach to selection bias defines selection bias as a spurious exposure-disease association within the study population that occurs when selection is a collider or a descendant of a collider on a causal path from exposure to disease in the eligible population. This definition covers only selection bias that can occur under the null hypothesis. Here, we propose a definition of selection bias in terms of potential outcomes that identifies selection bias whenever disease risks and exposure prevalences are distorted by the selection of study participants, not just a given measure of association (as in the traditional approach) or all measures of association (as in the structural approach). This definition is nonparametric, so it can be analyzed using causal graphs both under and away from the null. It unifies the theoretical frameworks used to understand selection bias and confounding, explicitly links selection to the estimation of causal effects, distinguishes clearly between internal and external validity, and simplifies the analysis of complex study designs.

In visual interactive labeling, users iteratively assign labels to data items until the machine model reaches an acceptable accuracy. A crucial step of this process is to inspect the model's accuracy and decide whether it is necessary to label additional elements. In scenarios with no or very little labeled data, visual inspection of the predictions is required. Similarity-preserving scatterplots created through a dimensionality reduction algorithm are a common visualization that is used in these cases. Previous studies investigated the effects of layout and image complexity on tasks like labeling. However, model evaluation has not been studied systematically. We present the results of an experiment studying the influence of image complexity and visual grouping of images on model accuracy estimation. We found that users outperform traditional automated approaches when estimating a model's accuracy. Furthermore, while the complexity of images impacts the overall performance, the layout of the items in the plot has little to no effect on estimations.

We present a general methodology to construct triplewise independent sequences of random variables having a common but arbitrary marginal distribution $F$ (satisfying very mild conditions). For two specific sequences, we obtain in closed form the asymptotic distribution of the sample mean. It is non-Gaussian (and depends on the specific choice of $F$). This allows us to illustrate the extent of the 'failure' of the classical central limit theorem (CLT) under triplewise independence. Our methodology is simple and can also be used to create, for any integer $K$, new $K$-tuplewise independent sequences that are not mutually independent. For $K \geq 4$, it appears that the sequences created using our methodology do verify a CLT, and we explain heuristically why this is the case.

We investigate the computational performance of Artificial Neural Networks (ANNs) in semi-nonparametric instrumental variables (NPIV) models of high dimensional covariates that are relevant to empirical work in economics. We focus on efficient estimation of and inference on expectation functionals (such as weighted average derivatives) and use optimal criterion-based procedures (sieve minimum distance or SMD) and novel efficient score-based procedures (ES). Both these procedures use ANN to approximate the unknown function. Then, we provide a detailed practitioner's recipe for implementing these two classes of estimators. This involves the choice of tuning parameters both for the unknown functions (that include conditional expectations) but also for the choice of estimation of the optimal weights in SMD and the Riesz representers used with the ES estimators. Finally, we conduct a large set of Monte Carlo experiments that compares the finite-sample performance in complicated designs that involve a large set of regressors (up to 13 continuous), and various underlying nonlinearities and covariate correlations. Some of the takeaways from our results include: 1) tuning and optimization are delicate especially as the problem is nonconvex; 2) various architectures of the ANNs do not seem to matter for the designs we consider and given proper tuning, ANN methods perform well; 3) stable inferences are more difficult to achieve with ANN estimators; 4) optimal SMD based estimators perform adequately; 5) there seems to be a gap between implementation and approximation theory. Finally, we apply ANN NPIV to estimate average price elasticity and average derivatives in two demand examples.

Sequential Multiple-Assignment Randomized Trials (SMARTs) play an increasingly important role in psychological and behavioral health research. This experimental approach enables researchers to answer scientific questions about how best to sequence and match interventions to the unique and changing needs of individuals. A variety of sample size calculations have been developed in recent years, enabling researchers to plan SMARTs for addressing different types of scientific questions. However, relatively limited attention has been given to planning SMARTs with binary (dichotomous) outcomes, which often require higher sample sizes relative to continuous outcomes. Existing resources for estimating sample size requirements for SMARTs with binary outcomes do not consider the potential ability to improve power by including a baseline measurement and/or multiple longitudinal measurements. The current paper addresses this issue by providing sample size formulas for longitudinal binary outcomes and exploring their performance via simulations.

To solve complex real-world problems with reinforcement learning, we cannot rely on manually specified reward functions. Instead, we can have humans communicate an objective to the agent directly. In this work, we combine two approaches to learning from human feedback: expert demonstrations and trajectory preferences. We train a deep neural network to model the reward function and use its predicted reward to train an DQN-based deep reinforcement learning agent on 9 Atari games. Our approach beats the imitation learning baseline in 7 games and achieves strictly superhuman performance on 2 games without using game rewards. Additionally, we investigate the goodness of fit of the reward model, present some reward hacking problems, and study the effects of noise in the human labels.

Discrete random structures are important tools in Bayesian nonparametrics and the resulting models have proven effective in density estimation, clustering, topic modeling and prediction, among others. In this paper, we consider nested processes and study the dependence structures they induce. Dependence ranges between homogeneity, corresponding to full exchangeability, and maximum heterogeneity, corresponding to (unconditional) independence across samples. The popular nested Dirichlet process is shown to degenerate to the fully exchangeable case when there are ties across samples at the observed or latent level. To overcome this drawback, inherent to nesting general discrete random measures, we introduce a novel class of latent nested processes. These are obtained by adding common and group-specific completely random measures and, then, normalising to yield dependent random probability measures. We provide results on the partition distributions induced by latent nested processes, and develop an Markov Chain Monte Carlo sampler for Bayesian inferences. A test for distributional homogeneity across groups is obtained as a by product. The results and their inferential implications are showcased on synthetic and real data.