Conformal prediction methods enjoy strong theoretical and empirical predictive inference performance, provided the data is exchangeable, and predictors are trained in a memoryless fashion. However, these assumptions and constraints are impractical in many real-data settings, such as time series (where temporal dependence violates exchangeability, and where memoryless predictors will inevitably have poor predictive accuracy). Recent work shows that the split conformal prediction method is robust to these issues of memory-based predictors and deviations from exchangeability that are common features of time-series data. However, since using sample splitting can lead to lower accuracy, this motivates asking whether other predictive inference methods (that do not rely on data splitting) could also be reliably used in the time series setting. In this work, we show that the vanilla leave-one-out jackknife can suffer an arbitrary loss of coverage even in canonical time series models with mild temporal dependence. As a remedy, we propose a careful modification tailored to such settings, which we term the \emph{leave-a-window-out} (LWO) method, and show that it can achieve valid coverage provided that the model-fitting procedure satisfies mild stability properties. Our proofs are based on quantifying the degree to which the data departs from \emph{cyclic exchangeability}, and we introduce new coefficients to measure the extent of this departure. Experiments on time series data demonstrate that our LWO method often enjoys valid coverage when the vanilla jackknife fails to cover, while producing much narrower intervals than split conformal prediction.

Obtaining reliable inferences with traditional difference-in-differences (DiD) methods can be difficult. Problems can arise when both outcomes and errors are serially correlated, when there are few clusters or few treated clusters, when cluster sizes vary greatly, and in various other cases. In recent years, recognition of the ``staggered adoption'' problem has shifted the focus away from inference towards consistent estimation of treatment effects. One of the most popular new estimators is the CSDID procedure of Callaway and Sant'Anna (2021). We find that the issues of over-rejection with few clusters and/or few treated clusters are at least as severe for CSDID as for traditional DiD methods. We also propose using a cluster jackknife for inference with CSDID, which simulations suggest greatly improves inference. We provide software packages in Stata csdidjack and R didjack to calculate cluster-jackknife standard errors easily.

This manuscript proposes to extend the information set of time-series regression trees with latent stationary factors extracted via state-space methods. First, it allows to handle predictors that exhibit measurement error, non-stationary trends, seasonality and/or irregularities such as missing observations. Second, it gives a transparent way for using domain-specific theory to inform time-series regression trees. As a byproduct, this technique sets the foundations for structuring powerful ensembles. Their real-world applicability is studied under the lenses of empirical macro-finance. Keywords: Ensemble learning, Factor models, State-space models, Time series, Unobserved components.Introduction In time series, the simplicity of regression trees (Morgan and Sonquist, 1963; Breiman et al., 1984; Quinlan, 1986) comes at a cost: irregularities, complicated periodic patterns and non-stationary trends cannot be explicitly modelled, and this is unfortunate given that many real-world examples are subject to them. Following, in spirit, Harvey et al. (1998), this paper proposes to pre-process problematic predictors using state-space representations general enough to deal with all these complexities at once. This operation can be thought as an automated feature engineering process that extracts stationary patterns hidden across multiple predictors, while handling problematic data characteristics. Besides, when the state-space representation is compatible with domain-specific theory, this becomes a transparent way for extracting signals with structural interpretation. The resulting stationary common components, referred hereinbelow as stationary dynamic factors, are then employed as regular predictors for standard time-series regression trees. This manuscript calls them factor-augmented regression trees to stress their dependence on latent components. I thank Matteo Barigozzi and Kostas Kalogeropoulos for their valuable suggestions and supervision; Serena Lariccia and Qiwei Yao for their helpful comments on a preliminary draft of this article.

Crucial for building trust in deep learning models for critical real-world applications is efficient and theoretically sound uncertainty quantification, a task that continues to be challenging. Useful uncertainty information is expected to have two key properties: It should be valid (guaranteeing coverage) and discriminative (more uncertain when the expected risk is high). Moreover, when combined with deep learning (DL) methods, it should be scalable and affect the DL model performance minimally. Most existing Bayesian methods lack frequentist coverage guarantees and usually affect model performance. The few available frequentist methods are rarely discriminative and/or violate coverage guarantees due to unrealistic assumptions. Moreover, many methods are expensive or require substantial modifications to the base neural network. Building upon recent advances in conformal prediction and leveraging the classical idea of kernel regression, we propose Locally Valid and Discriminative confidence intervals (LVD), a simple, efficient and lightweight method to construct discriminative confidence intervals (CIs) for almost any DL model. With no assumptions on the data distribution, such CIs also offer finite-sample local coverage guarantees (contrasted to the simpler marginal coverage). Using a diverse set of datasets, we empirically verify that besides being the only locally valid method, LVD also exceeds or matches the performance (including coverage rate and prediction accuracy) of existing uncertainty quantification methods, while offering additional benefits in scalability and flexibility.

The primary objective of supervised learning is to develop models that generalize robustly to unseen data. Benchmark test sets provide a proxy for out-of-sample performance, but can outlive their usefulness in some cases. For example, evaluating on benchmarks alone may steer us towards models that adaptively overfit [Reu03; RFR08; Dwo 15] to the finite test set and do not generalize. Alternatively, we might select for models that are sensitive to insignificant aspects of the dataset creation process and thus do not generalize robustly (e.g., models that are sensitive to the exact set of humans who annotated the test set). To diagnose these issues, recent work has generated new, previously "unseen" testbeds for standard datasets through a process known as dataset replication. Though not yet widespread in machine learning, dataset replication is a natural analogue to experimental replication studies in the natural sciences (cf.

Deep learning models achieve high predictive accuracy across a broad spectrum of tasks, but rigorously quantifying their predictive uncertainty remains challenging. Usable estimates of predictive uncertainty should (1) cover the true prediction targets with high probability, and (2) discriminate between high- and low-confidence prediction instances. Existing methods for uncertainty quantification are based predominantly on Bayesian neural networks; these may fall short of (1) and (2) -- i.e., Bayesian credible intervals do not guarantee frequentist coverage, and approximate posterior inference undermines discriminative accuracy. In this paper, we develop the discriminative jackknife (DJ), a frequentist procedure that utilizes influence functions of a model's loss functional to construct a jackknife (or leave-one-out) estimator of predictive confidence intervals. The DJ satisfies (1) and (2), is applicable to a wide range of deep learning models, is easy to implement, and can be applied in a post-hoc fashion without interfering with model training or compromising its accuracy. Experiments demonstrate that DJ performs competitively compared to existing Bayesian and non-Bayesian regression baselines.

Recurrent neural networks (RNNs) are instrumental in modelling sequential and time-series data. Yet, when using RNNs to inform decision-making, predictions by themselves are not sufficient; we also need estimates of predictive uncertainty. Existing approaches for uncertainty quantification in RNNs are based predominantly on Bayesian methods; these are computationally prohibitive, and require major alterations to the RNN architecture and training. Capitalizing on ideas from classical jackknife resampling, we develop a frequentist alternative that: (a) does not interfere with model training or compromise its accuracy, (b) applies to any RNN architecture, and (c) provides theoretical coverage guarantees on the estimated uncertainty intervals. Our method derives predictive uncertainty from the variability of the (jackknife) sampling distribution of the RNN outputs, which is estimated by repeatedly deleting blocks of (temporally-correlated) training data, and collecting the predictions of the RNN re-trained on the remaining data. To avoid exhaustive re-training, we utilize influence functions to estimate the effect of removing training data blocks on the learned RNN parameters. Using data from a critical care setting, we demonstrate the utility of uncertainty quantification in sequential decision-making.

The Internet is a giant, directed network of webpages pointing to other webpages. Facebook is an undirected network built via friendships between users. The ecological web is a directed network of different species with edges specified by'who-eats-whom' relationships. Protein-protein interactions are undirected networks consisting of pairs of baitprey proteins that bind to each other during coaffinity purification experiments arising in mass spectrometry analysis. In these application areas, it is often of interest to characterize a network using statistics such as the clustering coefficient, triangle density, or principal eigenvalues. There has been a substantial amount of work on approximating these quantities with small error on massive networks Assadi et al. (2018); Eden et al. (2017); Feige (2006); Goldreich and Ron (2008); Gonen et al. (2010); Kallaugher et al. (2019).

This article proposes a generalisation of the delete-$d$ jackknife to solve hyperparameter selection problems for time series. This novel technique is compatible with dependent data since it substitutes the jackknife removal step with a fictitious deletion, wherein observed datapoints are replaced with artificial missing values. In order to emphasise this point, I called this methodology artificial delete-$d$ jackknife. As an illustration, it is used to regulate vector autoregressions with an elastic-net penalty on the coefficients. A software implementation, ElasticNetVAR.jl, is available on GitHub.

Resampling is a way to reuse data to generate new, hypothetical samples (called resamples) that are representative of an underlying population. Two popular tools are the bootstrap and jackknife. Although they have many similarities (e.g. they both can estimate precision for an estimator θ), they do have a few notable differences. Bootstrapping is the most popular resampling method today. It uses sampling with replacement to estimate the sampling distribution for a desired estimator.