In quantitative genetics, statistical modeling techniques are used to facilitate advances in the understanding of which genes underlie agronomically important traits and have enabled the use of genome-wide markers to accelerate genetic gain. The logistic regression model is a statistically optimal approach for quantitative genetics analysis of binary traits. To encourage more widespread use of the logistic model in such analyses, efforts need to be made to address separation, which occurs whenever a specific combination of predictors can perfectly predict the value of a binary trait. Data separation is especially prevalent in applications where the number of predictors is near the sample size. In this study we motivate a logistic model that is robust to separation, and we develop a novel prediction procedure for this robust model that is appropriate when separation exists. We show that this robust model offers superior inferences and comparable predictions to existing approaches while remaining true to the logistic model. This is an improvement to previously existing approaches which treats separation as a modeling shortcoming and not an antagonistic data configuration. Previous approaches, therefore, change the modeling paradigm to consider separation that, before our robust model exists, is problematic to logistic models. Our comparisons are conducted on several didactic examples and a genomics study on the kernel color in maize. The ensuing analyses reaffirm the billed superior inferences and comparable predictive performance of our robust model. Therefore, our approach provides scientists with an appropriate statistical modeling framework for analyses involving agronomically important binary traits.
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We derive general, yet simple, sharp bounds on the size of the omitted variable bias for a broad class of causal parameters that can be identified as linear functionals of the conditional expectation function of the outcome. Such functionals encompass many of the traditional targets of investigation in causal inference studies, such as, for example, (weighted) average of potential outcomes, average treatment effects (including subgroup effects, such as the effect on the treated), (weighted) average derivatives, and policy effects from shifts in covariate distribution -- all for general, nonparametric causal models. Our construction relies on the Riesz-Frechet representation of the target functional. Specifically, we show how the bound on the bias depends only on the additional variation that the latent variables create both in the outcome and in the Riesz representer for the parameter of interest. Moreover, in many important cases (e.g, average treatment effects in partially linear models, or in nonseparable models with a binary treatment) the bound is shown to depend on two easily interpretable quantities: the nonparametric partial $R^2$ (Pearson's "correlation ratio") of the unobserved variables with the treatment and with the outcome. Therefore, simple plausibility judgments on the maximum explanatory power of omitted variables (in explaining treatment and outcome variation) are sufficient to place overall bounds on the size of the bias. Finally, leveraging debiased machine learning, we provide flexible and efficient statistical inference methods to estimate the components of the bounds that are identifiable from the observed distribution.
Unmeasured covariates constitute one of the important problems in causal inference. Even if there are some unmeasured covariates, some instrumental variable methods such as a two-stage residual inclusion (2SRI) estimator, or a limited-information maximum likelihood (LIML) estimator can obtain an unbiased estimate for causal effects despite there being nonlinear outcomes such as binary outcomes; however, it requires that we specify not only a correct outcome model but also a correct treatment model. Therefore, detecting correct models is an important process. In this paper, we propose two model selection procedures: AIC-type and BIC-type, and confirm their properties. The proposed model selection procedures are based on a LIML estimator. We prove that a proposed BIC-type model selection procedure has model selection consistency, and confirm their properties of the proposed model selection procedures through simulation datasets.
In many practical settings control decisions must be made under partial/imperfect information about the evolution of a relevant state variable. Partially Observable Markov Decision Processes (POMDPs) is a relatively well-developed framework for modeling and analyzing such problems. In this paper we consider the structural estimation of the primitives of a POMDP model based upon the observable history of the process. We analyze the structural properties of POMDP model with random rewards and specify conditions under which the model is identifiable without knowledge of the state dynamics. We consider a soft policy gradient algorithm to compute a maximum likelihood estimator and provide a finite-time characterization of convergence to a stationary point. We illustrate the estimation methodology with an application to optimal equipment replacement. In this context, replacement decisions must be made under partial/imperfect information on the true state (i.e. condition of the equipment). We use synthetic and real data to highlight the robustness of the proposed methodology and characterize the potential for misspecification when partial state observability is ignored.
Variable selection is an important statistical problem. This problem becomes more challenging when the candidate predictors are of mixed type (e.g. continuous and binary) and impact the response variable in nonlinear and/or non-additive ways. In this paper, we review existing variable selection approaches for the Bayesian additive regression trees (BART) model, a nonparametric regression model, which is flexible enough to capture the interactions between predictors and nonlinear relationships with the response. An emphasis of this review is on the capability of identifying relevant predictors. We also propose two variable importance measures which can be used in a permutation-based variable selection approach, and a backward variable selection procedure for BART. We present simulations demonstrating that our approaches exhibit improved performance in terms of the ability to recover all the relevant predictors in a variety of data settings, compared to existing BART-based variable selection methods.
An N-of-1 trial is a multi-period crossover trial performed in a single individual, with a primary goal to estimate treatment effect on the individual instead of population-level mean responses. As in a conventional crossover trial, it is critical to understand carryover effects of the treatment in an N-of-1 trial, especially when no washout periods between treatment periods are instituted to reduce trial duration. To deal with this issue in situations where high volume of measurements is made during the study, we introduce a novel Bayesian distributed lag model that facilitates the estimation of carryover effects, while accounting for temporal correlations using an autoregressive model. Specifically, we propose a prior variance-covariance structure on the lag coefficients to address collinearity caused by the fact that treatment exposures are typically identical on successive days. A connection between the proposed Bayesian model and penalized regression is noted. Simulation results demonstrate that the proposed model substantially reduces the root mean squared error in the estimation of carryover effects and immediate effects when compared to other existing methods, while being comparable in the estimation of the total effects. We also apply the proposed method to assess the extent of carryover effects of light therapies in relieving depressive symptoms in cancer survivors.
The ability to accurately estimate depth information is crucial for many autonomous applications to recognize the surrounded environment and predict the depth of important objects. One of the most recently used techniques is monocular depth estimation where the depth map is inferred from a single image. This paper improves the self-supervised deep learning techniques to perform accurate generalized monocular depth estimation. The main idea is to train the deep model to take into account a sequence of the different frames, each frame is geotagged with its location information. This makes the model able to enhance depth estimation given area semantics. We demonstrate the effectiveness of our model to improve depth estimation results. The model is trained in a realistic environment and the results show improvements in the depth map after adding the location data to the model training phase.
The dominating NLP paradigm of training a strong neural predictor to perform one task on a specific dataset has led to state-of-the-art performance in a variety of applications (eg. sentiment classification, span-prediction based question answering or machine translation). However, it builds upon the assumption that the data distribution is stationary, ie. that the data is sampled from a fixed distribution both at training and test time. This way of training is inconsistent with how we as humans are able to learn from and operate within a constantly changing stream of information. Moreover, it is ill-adapted to real-world use cases where the data distribution is expected to shift over the course of a model's lifetime. The first goal of this thesis is to characterize the different forms this shift can take in the context of natural language processing, and propose benchmarks and evaluation metrics to measure its effect on current deep learning architectures. We then proceed to take steps to mitigate the effect of distributional shift on NLP models. To this end, we develop methods based on parametric reformulations of the distributionally robust optimization framework. Empirically, we demonstrate that these approaches yield more robust models as demonstrated on a selection of realistic problems. In the third and final part of this thesis, we explore ways of efficiently adapting existing models to new domains or tasks. Our contribution to this topic takes inspiration from information geometry to derive a new gradient update rule which alleviate catastrophic forgetting issues during adaptation.
Classification tasks are usually analysed and improved through new model architectures or hyperparameter optimisation but the underlying properties of datasets are discovered on an ad-hoc basis as errors occur. However, understanding the properties of the data is crucial in perfecting models. In this paper we analyse exactly which characteristics of a dataset best determine how difficult that dataset is for the task of text classification. We then propose an intuitive measure of difficulty for text classification datasets which is simple and fast to calculate. We show that this measure generalises to unseen data by comparing it to state-of-the-art datasets and results. This measure can be used to analyse the precise source of errors in a dataset and allows fast estimation of how difficult a dataset is to learn. We searched for this measure by training 12 classical and neural network based models on 78 real-world datasets, then use a genetic algorithm to discover the best measure of difficulty. Our difficulty-calculating code ( //github.com/Wluper/edm ) and datasets ( //data.wluper.com ) are publicly available.
In this work, we compare three different modeling approaches for the scores of soccer matches with regard to their predictive performances based on all matches from the four previous FIFA World Cups 2002 - 2014: Poisson regression models, random forests and ranking methods. While the former two are based on the teams' covariate information, the latter method estimates adequate ability parameters that reflect the current strength of the teams best. Within this comparison the best-performing prediction methods on the training data turn out to be the ranking methods and the random forests. However, we show that by combining the random forest with the team ability parameters from the ranking methods as an additional covariate we can improve the predictive power substantially. Finally, this combination of methods is chosen as the final model and based on its estimates, the FIFA World Cup 2018 is simulated repeatedly and winning probabilities are obtained for all teams. The model slightly favors Spain before the defending champion Germany. Additionally, we provide survival probabilities for all teams and at all tournament stages as well as the most probable tournament outcome.
We propose a new method of estimation in topic models, that is not a variation on the existing simplex finding algorithms, and that estimates the number of topics K from the observed data. We derive new finite sample minimax lower bounds for the estimation of A, as well as new upper bounds for our proposed estimator. We describe the scenarios where our estimator is minimax adaptive. Our finite sample analysis is valid for any number of documents (n), individual document length (N_i), dictionary size (p) and number of topics (K), and both p and K are allowed to increase with n, a situation not handled well by previous analyses. We complement our theoretical results with a detailed simulation study. We illustrate that the new algorithm is faster and more accurate than the current ones, although we start out with a computational and theoretical disadvantage of not knowing the correct number of topics K, while we provide the competing methods with the correct value in our simulations.
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