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Observational studies are the primary source of data for causal inference, but it is challenging when existing unmeasured confounding. Missing data problems are also common in observational studies. How to obtain the causal effects from the nonignorable missing data with unmeasured confounding is a challenge. In this paper, we consider that how to obtain complier average causal effect with unmeasured confounding from the nonignorable missing outcomes. We propose an auxiliary variable which plays two roles simultaneously, the one is the shadow variable for identification and the other is the instrumental variable for inference. We also illustrate some difference between some missing outcomes mechanisms in the previous work and the shadow variable assumption. We give a causal diagram to illustrate this description. Under such a setting, we present a general condition for nonparametric identification of the full data law from the nonignorable missing outcomes with this auxiliary variable. For inference, firstly, we recover the mean value of the outcome based on the generalized method of moments. Secondly, we propose an estimator to adjust for the unmeasured confounding to obtain complier average causal effect. We also establish the asymptotic results of the estimated parameters. We evaluate its performance via simulations and apply it to a real-life dataset about a political analysis.

In causal inference, sensitivity analysis is important to assess the robustness of study conclusions to key assumptions. We perform sensitivity analysis of the assumption that missing outcomes are missing completely at random. We follow a Bayesian approach, which is nonparametric for the outcome distribution and can be combined with an informative prior on the sensitivity parameter. We give insight in the posterior and provide theoretical guarantees in the form of Bernstein-von Mises theorems for estimating the mean outcome. We study different parametrisations of the model involving Dirichlet process priors on the distribution of the outcome and on the distribution of the outcome conditional on the subject being treated. We show that these parametrisations incorporate a prior on the sensitivity parameter in different ways and discuss the relative merits. We also present a simulation study, showing the performance of the methods in finite sample scenarios.

A well-known problem when learning from user clicks are inherent biases prevalent in the data, such as position or trust bias. Click models are a common method for extracting information from user clicks, such as document relevance in web search, or to estimate click biases for downstream applications such as counterfactual learning-to-rank, ad placement, or fair ranking. Recent work shows that the current evaluation practices in the community fail to guarantee that a well-performing click model generalizes well to downstream tasks in which the ranking distribution differs from the training distribution, i.e., under covariate shift. In this work, we propose an evaluation metric based on conditional independence testing to detect a lack of robustness to covariate shift in click models. We introduce the concept of debiasedness and a metric for measuring it. We prove that debiasedness is a necessary condition for recovering unbiased and consistent relevance scores and for the invariance of click prediction under covariate shift. In extensive semi-synthetic experiments, we show that our proposed metric helps to predict the downstream performance of click models under covariate shift and is useful in an off-policy model selection setting.

Existing risk-aware multi-armed bandit models typically focus on risk measures of individual options such as variance. As a result, they cannot be directly applied to important real-world online decision making problems with correlated options. In this paper, we propose a novel Continuous Mean-Covariance Bandit (CMCB) model to explicitly take into account option correlation. Specifically, in CMCB, there is a learner who sequentially chooses weight vectors on given options and observes random feedback according to the decisions. The agent's objective is to achieve the best trade-off between reward and risk, measured with option covariance. To capture different reward observation scenarios in practice, we consider three feedback settings, i.e., full-information, semi-bandit and full-bandit feedback. We propose novel algorithms with optimal regrets (within logarithmic factors), and provide matching lower bounds to validate their optimalities. The experimental results also demonstrate the superiority of our algorithms. To the best of our knowledge, this is the first work that considers option correlation in risk-aware bandits and explicitly quantifies how arbitrary covariance structures impact the learning performance. The novel analytical techniques we developed for exploiting the estimated covariance to build concentration and bounding the risk of selected actions based on sampling strategy properties can likely find applications in other bandit analysis and be of independent interests.

We investigate the evidence/flexibility (i.e., "Occam") paradigm and demonstrate the theoretical and empirical consistency of Bayesian evidence for the task of determining an appropriate generative model for network data. This model selection framework involves determining a collection of candidate models, equipping each of these models' parameters with prior distributions derived via the encompassing priors method, and computing or approximating each models' evidence. We demonstrate how such a criterion may be used to select the most suitable model among the Erd\"os-R\`enyi (ER) model, independent edge (IE) model, and a special one-parameter low-rank stochastic blockmodel (SBM) with known memberships. The Erd\"os-R\`enyi may be considered as being linearly nested within IE, a fact which permits exponential family results. The uniparametric SBM is not so ideal, so we propose a numerical method to approximate the evidence. We apply this paradigm to brain connectome data. Future work necessitates deriving and equipping additional candidate random graph models with appropriate priors so they may be included in the paradigm.

FM-indexes are a crucial data structure in DNA alignment, for example, but searching with them usually takes at least one random access per character in the query pattern. Ferragina and Fischer observed in 2007 that word-based indexes often use fewer random accesses than character-based indexes, and thus support faster searches. Since DNA lacks natural word-boundaries, however, it is necessary to parse it somehow before applying word-based FM-indexing. Last year, Deng et al.\ proposed parsing genomic data by induced suffix sorting, and showed the resulting word-based FM-indexes support faster counting queries than standard FM-indexes when patterns are a few thousand characters or longer. In this paper we show that using prefix-free parsing -- which takes parameters that let us tune the average length of the phrases -- instead of induced suffix sorting, gives a significant speedup for patterns of only a few hundred characters. We implement our method and demonstrate it is between 3 and 18 times faster than competing methods on queries to GRCh38. And was consistently faster on queries made to 25,000, 50,000 and 100,000 SARS-CoV-2 genomes. Hence, it is very clear that our method accelerates the performance of count over all state-of-the-art methods with a minor increase in the memory. Our source code is available at //github.com/marco-oliva/afm .

Applying simple linear regression models, an economist analysed a published dataset from an influential annual ranking in 2016 and 2017 of consumer outlets for Dutch New Herring and concluded that the ranking was manipulated. His finding was promoted by his university in national and international media, and this led to public outrage and ensuing discontinuation of the survey. We reconstitute the dataset, correcting errors and exposing features already important in a descriptive analysis of the data. The economist has continued his investigations, and in a follow-up publication repeats the same accusations. We point out errors in his reasoning and show that alleged evidence for deliberate manipulation of the ranking could easily be an artefact of specification errors. Temporal and spatial factors are both important and complex, and their effects cannot be captured using simple models, given the small sample sizes and many factors determining perceived taste of a food product.

When an exposure of interest is confounded by unmeasured factors, an instrumental variable (IV) can be used to identify and estimate certain causal contrasts. Identification of the marginal average treatment effect (ATE) from IVs relies on strong untestable structural assumptions. When one is unwilling to assert such structure, IVs can nonetheless be used to construct bounds on the ATE. Famously, Balke and Pearl (1997) proved tight bounds on the ATE for a binary outcome, in a randomized trial with noncompliance and no covariate information. We demonstrate how these bounds remain useful in observational settings with baseline confounders of the IV, as well as randomized trials with measured baseline covariates. The resulting bounds on the ATE are non-smooth functionals, and thus standard nonparametric efficiency theory is not immediately applicable. To remedy this, we propose (1) under a novel margin condition, influence function-based estimators of the bounds that can attain parametric convergence rates when the nuisance functions are modeled flexibly, and (2) estimators of smooth approximations of these bounds. We propose extensions to continuous outcomes, explore finite sample properties in simulations, and illustrate the proposed estimators in a randomized field experiment studying the effects of canvassing on resulting voter turnout.

The concept of causality plays an important role in human cognition . In the past few decades, causal inference has been well developed in many fields, such as computer science, medicine, economics, and education. With the advancement of deep learning techniques, it has been increasingly used in causal inference against counterfactual data. Typically, deep causal models map the characteristics of covariates to a representation space and then design various objective optimization functions to estimate counterfactual data unbiasedly based on the different optimization methods. This paper focuses on the survey of the deep causal models, and its core contributions are as follows: 1) we provide relevant metrics under multiple treatments and continuous-dose treatment; 2) we incorporate a comprehensive overview of deep causal models from both temporal development and method classification perspectives; 3) we assist a detailed and comprehensive classification and analysis of relevant datasets and source code.