Using a perturbation technique, we derive a new approximate filtering and smoothing methodology generalizing along different directions several existing approaches to robust filtering based on the score and the Hessian matrix of the observation density. The main advantages of the methodology can be summarized as follows: (i) it relaxes the critical assumption of a Gaussian prior distribution for the latent states underlying such approaches; (ii) can be applied to a general class of state-space models including univariate and multivariate location, scale and count data models; (iii) has a very simple structure based on forward-backward recursions similar to the Kalman filter and smoother; (iv) allows a straightforward computation of confidence bands around the state estimates reflecting the combination of parameter and filtering uncertainty. We show through an extensive Monte Carlo study that the mean square loss with respect to exact simulation-based methods is small in a wide range of scenarios. We finally illustrate empirically the application of the methodology to the estimation of stochastic volatility and correlations in financial time-series.
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Cardinality estimation methods based on probability distribution estimation have achieved high-precision estimation results compared to traditional methods. However, the most advanced methods suffer from high estimation costs due to the sampling method they use when dealing with range queries. Also, such a sampling method makes them difficult to differentiate, so the supervision signal from the query workload is difficult to train the model to improve the accuracy of cardinality estimation. In this paper, we propose a new hybrid and deterministic modeling approach (Duet) for the cardinality estimation problem which has better efficiency and scalability compared to previous approaches. Duet allows for direct cardinality estimation of range queries with significantly lower time and memory costs, as well as in a differentiable form. As the prediction process of this approach is differentiable, we can incorporate queries with larger model estimation errors into the training process to address the long-tail distribution problem of model estimation errors on high dimensional tables. We evaluate Duet on classical datasets and benchmarks, and the results prove the effectiveness of Duet.
We study error propagation in both an explicit and an implicit method for solving Volterra integro-differential equations. We determine the relationship between local and global errors. We derive upper bounds for the global error, and show that the global order for both methods is expected to be first-order. A few numerical examples illustrate our results.
The paper introduces methods to estimate a policy that achieves a pre-defined, outcome-oriented target and accounts for potential spillover effects in a block due to partial interference. Specifically, our policy, which we call the minimum resource threshold policy (MRTP), suggests the minimum fraction of treated units required within a block to meet or exceed the target level of the outcome. We estimate the MRTP from empirical risk minimization associated with a novel, nonparametric, doubly robust loss function. We then characterize the statistical property of the estimated MRTP in terms of the excess risk bound. We apply our methodology to design a water, sanitation, and hygiene allocation policy for Senegal with the goal of increasing the proportion of households with no children experiencing diarrhea to a level exceeding a specified threshold. Our policy outperforms competing policies and offers new approaches to design allocation policies, especially in international development for communicable diseases.
Perfect synchronization in distributed machine learning problems is inefficient and even impossible due to the existence of latency, package losses and stragglers. We propose a Robust Fully-Asynchronous Stochastic Gradient Tracking method (R-FAST), where each device performs local computation and communication at its own pace without any form of synchronization. Different from existing asynchronous distributed algorithms, R-FAST can eliminate the impact of data heterogeneity across devices and allow for packet losses by employing a robust gradient tracking strategy that relies on properly designed auxiliary variables for tracking and buffering the overall gradient vector. More importantly, the proposed method utilizes two spanning-tree graphs for communication so long as both share at least one common root, enabling flexible designs in communication architectures. We show that R-FAST converges in expectation to a neighborhood of the optimum with a geometric rate for smooth and strongly convex objectives; and to a stationary point with a sublinear rate for general non-convex settings. Extensive experiments demonstrate that R-FAST runs 1.5-2 times faster than synchronous benchmark algorithms, such as Ring-AllReduce and D-PSGD, while still achieving comparable accuracy, and outperforms existing asynchronous SOTA algorithms, such as AD-PSGD and OSGP, especially in the presence of stragglers.
Recently, there has been great interest in estimating the conditional average treatment effect using flexible machine learning methods. However, in practice, investigators often have working hypotheses about effect heterogeneity across pre-defined subgroups of study units, which we call the groupwise approach. The paper compares two modern ways to estimate groupwise treatment effects, a nonparametric approach and a semiparametric approach, with the goal of better informing practice. Specifically, we compare (a) the underlying assumptions, (b) efficiency and adaption to the underlying data generating models, and (c) a way to combine the two approaches. We also discuss how to test a key assumption concerning the semiparametric estimator and to obtain cluster-robust standard errors if study units in the same subgroups are correlated. We demonstrate our findings by conducting simulation studies and reanalyzing the Early Childhood Longitudinal Study.
This PhD thesis contains several contributions to the field of statistical causal modeling. Statistical causal models are statistical models embedded with causal assumptions that allow for the inference and reasoning about the behavior of stochastic systems affected by external manipulation (interventions). This thesis contributes to the research areas concerning the estimation of causal effects, causal structure learning, and distributionally robust (out-of-distribution generalizing) prediction methods. We present novel and consistent linear and non-linear causal effects estimators in instrumental variable settings that employ data-dependent mean squared prediction error regularization. Our proposed estimators show, in certain settings, mean squared error improvements compared to both canonical and state-of-the-art estimators. We show that recent research on distributionally robust prediction methods has connections to well-studied estimators from econometrics. This connection leads us to prove that general K-class estimators possess distributional robustness properties. We, furthermore, propose a general framework for distributional robustness with respect to intervention-induced distributions. In this framework, we derive sufficient conditions for the identifiability of distributionally robust prediction methods and present impossibility results that show the necessity of several of these conditions. We present a new structure learning method applicable in additive noise models with directed trees as causal graphs. We prove consistency in a vanishing identifiability setup and provide a method for testing substructure hypotheses with asymptotic family-wise error control that remains valid post-selection. Finally, we present heuristic ideas for learning summary graphs of nonlinear time-series models.
The essence of multivariate sequential learning is all about how to extract dependencies in data. These data sets, such as hourly medical records in intensive care units and multi-frequency phonetic time series, often time exhibit not only strong serial dependencies in the individual components (the "marginal" memory) but also non-negligible memories in the cross-sectional dependencies (the "joint" memory). Because of the multivariate complexity in the evolution of the joint distribution that underlies the data generating process, we take a data-driven approach and construct a novel recurrent network architecture, termed Memory-Gated Recurrent Networks (mGRN), with gates explicitly regulating two distinct types of memories: the marginal memory and the joint memory. Through a combination of comprehensive simulation studies and empirical experiments on a range of public datasets, we show that our proposed mGRN architecture consistently outperforms state-of-the-art architectures targeting multivariate time series.
The recent proliferation of knowledge graphs (KGs) coupled with incomplete or partial information, in the form of missing relations (links) between entities, has fueled a lot of research on knowledge base completion (also known as relation prediction). Several recent works suggest that convolutional neural network (CNN) based models generate richer and more expressive feature embeddings and hence also perform well on relation prediction. However, we observe that these KG embeddings treat triples independently and thus fail to cover the complex and hidden information that is inherently implicit in the local neighborhood surrounding a triple. To this effect, our paper proposes a novel attention based feature embedding that captures both entity and relation features in any given entity's neighborhood. Additionally, we also encapsulate relation clusters and multihop relations in our model. Our empirical study offers insights into the efficacy of our attention based model and we show marked performance gains in comparison to state of the art methods on all datasets.
Object tracking is challenging as target objects often undergo drastic appearance changes over time. Recently, adaptive correlation filters have been successfully applied to object tracking. However, tracking algorithms relying on highly adaptive correlation filters are prone to drift due to noisy updates. Moreover, as these algorithms do not maintain long-term memory of target appearance, they cannot recover from tracking failures caused by heavy occlusion or target disappearance in the camera view. In this paper, we propose to learn multiple adaptive correlation filters with both long-term and short-term memory of target appearance for robust object tracking. First, we learn a kernelized correlation filter with an aggressive learning rate for locating target objects precisely. We take into account the appropriate size of surrounding context and the feature representations. Second, we learn a correlation filter over a feature pyramid centered at the estimated target position for predicting scale changes. Third, we learn a complementary correlation filter with a conservative learning rate to maintain long-term memory of target appearance. We use the output responses of this long-term filter to determine if tracking failure occurs. In the case of tracking failures, we apply an incrementally learned detector to recover the target position in a sliding window fashion. Extensive experimental results on large-scale benchmark datasets demonstrate that the proposed algorithm performs favorably against the state-of-the-art methods in terms of efficiency, accuracy, and robustness.
Object detection typically assumes that training and test data are drawn from an identical distribution, which, however, does not always hold in practice. Such a distribution mismatch will lead to a significant performance drop. In this work, we aim to improve the cross-domain robustness of object detection. We tackle the domain shift on two levels: 1) the image-level shift, such as image style, illumination, etc, and 2) the instance-level shift, such as object appearance, size, etc. We build our approach based on the recent state-of-the-art Faster R-CNN model, and design two domain adaptation components, on image level and instance level, to reduce the domain discrepancy. The two domain adaptation components are based on H-divergence theory, and are implemented by learning a domain classifier in adversarial training manner. The domain classifiers on different levels are further reinforced with a consistency regularization to learn a domain-invariant region proposal network (RPN) in the Faster R-CNN model. We evaluate our newly proposed approach using multiple datasets including Cityscapes, KITTI, SIM10K, etc. The results demonstrate the effectiveness of our proposed approach for robust object detection in various domain shift scenarios.
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