We extend the idea of automated debiased machine learning to the dynamic treatment regime and more generally to nested functionals. We show that the multiply robust formula for the dynamic treatment regime with discrete treatments can be re-stated in terms of a recursive Riesz representer characterization of nested mean regressions. We then apply a recursive Riesz representer estimation learning algorithm that estimates de-biasing corrections without the need to characterize how the correction terms look like, such as for instance, products of inverse probability weighting terms, as is done in prior work on doubly robust estimation in the dynamic regime. Our approach defines a sequence of loss minimization problems, whose minimizers are the mulitpliers of the de-biasing correction, hence circumventing the need for solving auxiliary propensity models and directly optimizing for the mean squared error of the target de-biasing correction. We provide further applications of our approach to estimation of dynamic discrete choice models and estimation of long-term effects with surrogates.
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We explore unique considerations involved in fitting ML models to data with very high precision, as is often required for science applications. We empirically compare various function approximation methods and study how they scale with increasing parameters and data. We find that neural networks can often outperform classical approximation methods on high-dimensional examples, by auto-discovering and exploiting modular structures therein. However, neural networks trained with common optimizers are less powerful for low-dimensional cases, which motivates us to study the unique properties of neural network loss landscapes and the corresponding optimization challenges that arise in the high precision regime. To address the optimization issue in low dimensions, we develop training tricks which enable us to train neural networks to extremely low loss, close to the limits allowed by numerical precision.
Deep Learning (DL) methods have emerged as one of the most powerful tools for functional approximation and prediction. While the representation properties of DL have been well studied, uncertainty quantification remains challenging and largely unexplored. Data augmentation techniques are a natural approach to provide uncertainty quantification and to incorporate stochastic Monte Carlo search into stochastic gradient descent (SGD) methods. The purpose of our paper is to show that training DL architectures with data augmentation leads to efficiency gains. We use the theory of scale mixtures of normals to derive data augmentation strategies for deep learning. This allows variants of the expectation-maximization and MCMC algorithms to be brought to bear on these high dimensional nonlinear deep learning models. To demonstrate our methodology, we develop data augmentation algorithms for a variety of commonly used activation functions: logit, ReLU, leaky ReLU and SVM. Our methodology is compared to traditional stochastic gradient descent with back-propagation. Our optimization procedure leads to a version of iteratively re-weighted least squares and can be implemented at scale with accelerated linear algebra methods providing substantial improvement in speed. We illustrate our methodology on a number of standard datasets. Finally, we conclude with directions for future research.
Customer feedback can be an important signal for improving commercial machine translation systems. One solution for fixing specific translation errors is to remove the related erroneous training instances followed by re-training of the machine translation system, which we refer to as instance-specific data filtering. Influence functions (IF) have been shown to be effective in finding such relevant training examples for classification tasks such as image classification, toxic speech detection and entailment task. Given a probing instance, IF find influential training examples by measuring the similarity of the probing instance with a set of training examples in gradient space. In this work, we examine the use of influence functions for Neural Machine Translation (NMT). We propose two effective extensions to a state of the art influence function and demonstrate on the sub-problem of copied training examples that IF can be applied more generally than handcrafted regular expressions.
Many causal and structural effects depend on regressions. Examples include policy effects, average derivatives, regression decompositions, average treatment effects, causal mediation, and parameters of economic structural models. The regressions may be high dimensional, making machine learning useful. Plugging machine learners into identifying equations can lead to poor inference due to bias from regularization and/or model selection. This paper gives automatic debiasing for linear and nonlinear functions of regressions. The debiasing is automatic in using Lasso and the function of interest without the full form of the bias correction. The debiasing can be applied to any regression learner, including neural nets, random forests, Lasso, boosting, and other high dimensional methods. In addition to providing the bias correction we give standard errors that are robust to misspecification, convergence rates for the bias correction, and primitive conditions for asymptotic inference for estimators of a variety of estimators of structural and causal effects. The automatic debiased machine learning is used to estimate the average treatment effect on the treated for the NSW job training data and to estimate demand elasticities from Nielsen scanner data while allowing preferences to be correlated with prices and income.
We provide adaptive inference methods, based on $\ell_1$ regularization, for regular (semi-parametric) and non-regular (nonparametric) linear functionals of the conditional expectation function. Examples of regular functionals include average treatment effects, policy effects, and derivatives. Examples of non-regular functionals include average treatment effects, policy effects, and derivatives conditional on a covariate subvector fixed at a point. We construct a Neyman orthogonal equation for the target parameter that is approximately invariant to small perturbations of the nuisance parameters. To achieve this property, we include the Riesz representer for the functional as an additional nuisance parameter. Our analysis yields weak ``double sparsity robustness'': either the approximation to the regression or the approximation to the representer can be ``completely dense'' as long as the other is sufficiently ``sparse''. Our main results are non-asymptotic and imply asymptotic uniform validity over large classes of models, translating into honest confidence bands for both global and local parameters.
Debiased machine learning is a meta algorithm based on bias correction and sample splitting to calculate confidence intervals for functionals, i.e. scalar summaries, of machine learning algorithms. For example, an analyst may desire the confidence interval for a treatment effect estimated with a neural network. We provide a nonasymptotic debiased machine learning theorem that encompasses any global or local functional of any machine learning algorithm that satisfies a few simple, interpretable conditions. Formally, we prove consistency, Gaussian approximation, and semiparametric efficiency by finite sample arguments. The rate of convergence is $n^{-1/2}$ for global functionals, and it degrades gracefully for local functionals. Our results culminate in a simple set of conditions that an analyst can use to translate modern learning theory rates into traditional statistical inference. The conditions reveal a general double robustness property for ill posed inverse problems.
One common approach to detecting change-points is minimizing a cost function over possible numbers and locations of change-points. The framework includes several well-established procedures, such as the penalized likelihood and minimum description length. Such an approach requires finding the cost value repeatedly over different segments of the data set, which can be time-consuming when (i) the data sequence is long and (ii) obtaining the cost value involves solving a non-trivial optimization problem. This paper introduces a new sequential method (SE) that can be coupled with gradient descent (SeGD) and quasi-Newton's method (SeN) to find the cost value effectively. The core idea is to update the cost value using the information from previous steps without re-optimizing the objective function. The new method is applied to change-point detection in generalized linear models and penalized regression. Numerical studies show that the new approach can be orders of magnitude faster than the Pruned Exact Linear Time (PELT) method without sacrificing estimation accuracy.
A fundamental task in science is to design experiments that yield valuable insights about the system under study. Mathematically, these insights can be represented as a utility or risk function that shapes the value of conducting each experiment. We present PDBAL, a targeted active learning method that adaptively designs experiments to maximize scientific utility. PDBAL takes a user-specified risk function and combines it with a probabilistic model of the experimental outcomes to choose designs that rapidly converge on a high-utility model. We prove theoretical bounds on the label complexity of PDBAL and provide fast closed-form solutions for designing experiments with common exponential family likelihoods. In simulation studies, PDBAL consistently outperforms standard untargeted approaches that focus on maximizing expected information gain over the design space. Finally, we demonstrate the scientific potential of PDBAL through a study on a large cancer drug screen dataset where PDBAL quickly recovers the most efficacious drugs with a small fraction of the total number of experiments.
We propose a generalization of the synthetic control and synthetic interventions methodology to the dynamic treatment regime. We consider the estimation of unit-specific treatment effects from panel data collected via a dynamic treatment regime and in the presence of unobserved confounding. That is, each unit receives multiple treatments sequentially, based on an adaptive policy, which depends on a latent endogenously time-varying confounding state of the treated unit. Under a low-rank latent factor model assumption and a technical overlap assumption we propose an identification strategy for any unit-specific mean outcome under any sequence of interventions. The latent factor model we propose admits linear time-varying and time-invariant dynamical systems as special cases. Our approach can be seen as an identification strategy for structural nested mean models under a low-rank latent factor assumption on the blip effects. Our method, which we term "synthetic blip effects", is a backwards induction process, where the blip effect of a treatment at each period and for a target unit is recursively expressed as linear combinations of blip effects of a carefully chosen group of other units that received the designated treatment. Our work avoids the combinatorial explosion in the number of units that would be required by a vanilla application of prior synthetic control and synthetic intervention methods in such dynamic treatment regime settings.
We focus on the setting of contextual batched bandit (CBB), where a batch of rewards is observed from the environment in each episode. But the rewards of the non-executed actions are unobserved (i.e., partial-information feedbacks). Existing approaches for CBB usually ignore the rewards of the non-executed actions, resulting in feedback information being underutilized. In this paper, we propose an efficient reward imputation approach using sketching for CBB, which completes the unobserved rewards with the imputed rewards approximating the full-information feedbacks. Specifically, we formulate the reward imputation as a problem of imputation regularized ridge regression, which captures the feedback mechanisms of both the non-executed and executed actions. To reduce the time complexity of reward imputation, we solve the regression problem using randomized sketching. We prove that our reward imputation approach obtains a relative-error bound for sketching approximation, achieves an instantaneous regret with a controllable bias and a smaller variance than that without reward imputation, and enjoys a sublinear regret bound against the optimal policy. Moreover, we present two extensions of our approach, including the rate-scheduled version and the version for nonlinear rewards, making our approach more feasible. Experimental results demonstrated that our approach can outperform the state-of-the-art baselines on synthetic and real-world datasets.
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