Completely randomized experiment is the gold standard for causal inference. When the covariate information for each experimental candidate is available, one typical way is to include them in covariate adjustments for more accurate treatment effect estimation. In this paper, we investigate this problem under the randomization-based framework, i.e., that the covariates and potential outcomes of all experimental candidates are assumed as deterministic quantities and the randomness comes solely from the treatment assignment mechanism. Under this framework, to achieve asymptotically valid inference, existing estimators usually require either (i) that the dimension of covariates $p$ grows at a rate no faster than $O(n^{3 / 4})$ as sample size $n \to \infty$; or (ii) certain sparsity constraints on the linear representations of potential outcomes constructed via possibly high-dimensional covariates. In this paper, we consider the moderately high-dimensional regime where $p$ is allowed to be in the same order of magnitude as $n$. We develop a novel debiased estimator with a corresponding inference procedure and establish its asymptotic normality under mild assumptions. Our estimator is model-free and does not require any sparsity constraint on potential outcome's linear representations. We also discuss its asymptotic efficiency improvements over the unadjusted treatment effect estimator under different dimensionality constraints. Numerical analysis confirms that compared to other regression adjustment based treatment effect estimators, our debiased estimator performs well in moderately high dimensions.
相關內容
Dealing with uncertainty in optimization parameters is an important and longstanding challenge. Typically, uncertain parameters are predicted accurately, and then a deterministic optimization problem is solved. However, the decisions produced by this so-called \emph{predict-then-optimize} procedure can be highly sensitive to uncertain parameters. In this work, we contribute to recent efforts in producing \emph{decision-focused} predictions, i.e., to build predictive models that are constructed with the goal of minimizing a \emph{regret} measure on the decisions taken with them. We begin by formulating the exact expected regret minimization as a pessimistic bilevel optimization model. Then, we establish NP-completeness of this problem, even in a heavily restricted case. Using duality arguments, we reformulate it as a non-convex quadratic optimization problem. Finally, we show various computational techniques to achieve tractability. We report extensive computational results on shortest-path instances with uncertain cost vectors. Our results indicate that our approach can improve training performance over the approach of Elmachtoub and Grigas (2022), a state-of-the-art method for decision-focused learning.
Logistic regression is a classical model for describing the probabilistic dependence of binary responses to multivariate covariates. We consider the predictive performance of the maximum likelihood estimator (MLE) for logistic regression, assessed in terms of logistic risk. We consider two questions: first, that of the existence of the MLE (which occurs when the dataset is not linearly separated), and second that of its accuracy when it exists. These properties depend on both the dimension of covariates and on the signal strength. In the case of Gaussian covariates and a well-specified logistic model, we obtain sharp non-asymptotic guarantees for the existence and excess logistic risk of the MLE. We then generalize these results in two ways: first, to non-Gaussian covariates satisfying a certain two-dimensional margin condition, and second to the general case of statistical learning with a possibly misspecified logistic model. Finally, we consider the case of a Bernoulli design, where the behavior of the MLE is highly sensitive to the parameter direction.
In real-world data, information is stored in extremely large feature vectors. These variables are typically correlated due to complex interactions involving many features simultaneously. Such correlations qualitatively correspond to semantic roles and are naturally recognized by both the human brain and artificial neural networks. This recognition enables, for instance, the prediction of missing parts of an image or text based on their context. We present a method to detect these correlations in high-dimensional data represented as binary numbers. We estimate the binary intrinsic dimension of a dataset, which quantifies the minimum number of independent coordinates needed to describe the data, and is therefore a proxy of semantic complexity. The proposed algorithm is largely insensitive to the so-called curse of dimensionality, and can therefore be used in big data analysis. We test this approach identifying phase transitions in model magnetic systems and we then apply it to the detection of semantic correlations of images and text inside deep neural networks.
Distinguishing two candidate models is a fundamental and practically important statistical problem. Error rate control is crucial to the testing logic but, in complex nonparametric settings, can be difficult to achieve, especially when the stopping rule that determines the data collection process is not available. This paper proposes an e-process construction based on the predictive recursion (PR) algorithm originally designed to recursively fit nonparametric mixture models. The resulting PRe-process affords anytime valid inference and is asymptotically efficient in the sense that its growth rate is first-order optimal relative to PR's mixture model.
We consider the nonparametric regression problem when the covariates are located on an unknown smooth compact submanifold of a Euclidean space. Under defining a random geometric graph structure over the covariates we analyze the asymptotic frequentist behaviour of the posterior distribution arising from Bayesian priors designed through random basis expansion in the graph Laplacian eigenbasis. Under Holder smoothness assumption on the regression function and the density of the covariates over the submanifold, we prove that the posterior contraction rates of such methods are minimax optimal (up to logarithmic factors) for any positive smoothness index.
We propose a tamed-adaptive Milstein scheme for stochastic differential equations in which the first-order derivatives of the coefficients are locally H\"older continuous of order $\alpha$. We show that the scheme converges in the $L_2$-norm with a rate of $(1+\alpha)/2$ over both finite intervals $[0, T]$ and the infinite interval $(0, +\infty)$, under certain growth conditions on the coefficients.
Mobile devices and the Internet of Things (IoT) devices nowadays generate a large amount of heterogeneous spatial-temporal data. It remains a challenging problem to model the spatial-temporal dynamics under privacy concern. Federated learning (FL) has been proposed as a framework to enable model training across distributed devices without sharing original data which reduce privacy concern. Personalized federated learning (PFL) methods further address data heterogenous problem. However, these methods don't consider natural spatial relations among nodes. For the sake of modeling spatial relations, Graph Neural Netowork (GNN) based FL approach have been proposed. But dynamic spatial-temporal relations among edge nodes are not taken into account. Several approaches model spatial-temporal dynamics in a centralized environment, while less effort has been made under federated setting. To overcome these challeges, we propose a novel Federated Adaptive Spatial-Temporal Attention (FedASTA) framework to model the dynamic spatial-temporal relations. On the client node, FedASTA extracts temporal relations and trend patterns from the decomposed terms of original time series. Then, on the server node, FedASTA utilize trend patterns from clients to construct adaptive temporal-spatial aware graph which captures dynamic correlation between clients. Besides, we design a masked spatial attention module with both static graph and constructed adaptive graph to model spatial dependencies among clients. Extensive experiments on five real-world public traffic flow datasets demonstrate that our method achieves state-of-art performance in federated scenario. In addition, the experiments made in centralized setting show the effectiveness of our novel adaptive graph construction approach compared with other popular dynamic spatial-temporal aware methods.
We show that confidence intervals in a variance component model, with asymptotically correct uniform coverage probability, can be obtained by inverting certain test-statistics based on the score for the restricted likelihood. The results apply in settings where the variance is near or at the boundary of the parameter set. Simulations indicate the proposed test-statistics are approximately pivotal and lead to confidence intervals with near-nominal coverage even in small samples. We illustrate our methods' application in spatially-resolved transcriptomics where we compute approximately 15,000 confidence intervals, used for gene ranking, in less than 4 minutes. In the settings we consider, the proposed method is between two and 28,000 times faster than popular alternatives, depending on how many confidence intervals are computed.
Accurate computation of robust estimates for extremal quantiles of empirical distributions is an essential task for a wide range of applicative fields, including economic policymaking and the financial industry. Such estimates are particularly critical in calculating risk measures, such as Growth-at-Risk (GaR). % and Value-at-Risk (VaR). This work proposes a conformal framework to estimate calibrated quantiles, and presents an extensive simulation study and a real-world analysis of GaR to examine its benefits with respect to the state of the art. Our findings show that CP methods consistently improve the calibration and robustness of quantile estimates at all levels. The calibration gains are appreciated especially at extremal quantiles, which are critical for risk assessment and where traditional methods tend to fall short. In addition, we introduce a novel property that guarantees coverage under the exchangeability assumption, providing a valuable tool for managing risks by quantifying and controlling the likelihood of future extreme observations.
We study the problem of modeling and inference for spatio-temporal count processes. Our approach uses parsimonious parameterisations of multivariate autoregressive count time series models, including possible regression on covariates. We control the number of parameters by specifying spatial neighbourhood structures for possibly huge matrices that take into account spatio-temporal dependencies. This work is motivated by real data applications which call for suitable models. Extensive simulation studies show that our approach yields reliable estimators.
注冊地址： 北京市海淀區羊坊店路18號2幢3層301-191