Least squares regression with heteroskedasticity and autocorrelation consistent (HAC) standard errors has proved very useful in cross section environments. However, several major difficulties, which are generally overlooked, must be confronted when transferring the HAC estimation technology to time series environments. First, in plausible time-series environments involving failure of strong exogeneity, OLS parameter estimates can be inconsistent, so that HAC inference fails even asymptotically. Second, most economic time series have strong autocorrelation, which renders HAC regression parameter estimates highly inefficient. Third, strong autocorrelation similarly renders HAC conditional predictions highly inefficient. Finally, The structure of popular HAC estimators is ill-suited for capturing the autoregressive autocorrelation typically present in economic time series, which produces large size distortions and reduced power in HACbased hypothesis testing, in all but the largest samples. We show that all four problems are largely avoided by the use of a simple dynamic regression procedure, which is easily implemented. We demonstrate the advantages of dynamic regression with detailed simulations covering a range of practical issues.
相關內容
Dimensionality reduction has always been one of the most significant and challenging problems in the analysis of high-dimensional data. In the context of time series analysis, our focus is on the estimation and inference of conditional mean and variance functions. By using central mean and variance dimension reduction subspaces that preserve sufficient information about the response, one can effectively estimate the unknown mean and variance functions of the time series. While the literature presents several approaches to estimate the time series central mean and variance subspaces (TS-CMS and TS-CVS), these methods tend to be computationally intensive and infeasible for practical applications. By employing the Fourier transform, we derive explicit estimators for TS-CMS and TS-CVS. These proposed estimators are demonstrated to be consistent, asymptotically normal, and efficient. Simulation studies have been conducted to evaluate the performance of the proposed method. The results show that our method is significantly more accurate and computationally efficient than existing methods. Furthermore, the method has been applied to the Canadian Lynx dataset.
Optimal transport aims to learn a mapping of sources to targets by minimizing the cost, which is typically defined as a function of distance. The solution to this problem consists of straight line segments optimally connecting sources to targets, and it does not exhibit branching. These optimal solutions are in stark contrast with both natural, and man-made transportation networks, where branching structures are prevalent. Here we discuss a fast heuristic branching method for optimal transport in networks, and we provide several applications.
Currently, matrix decomposition is one of the most widely used collaborative filtering algorithms by using factor decomposition to effectively deal with large-scale rating matrix. It mainly uses the interaction records between users and items to predict ratings. Based on the characteristic attributes of items and users, this paper proposes a new UISVD++ model that fuses the type attributes of movies and the age attributes of users into SVD++ framework. By projecting the age attribute into the user's implicit space and the type attribute into the item's implicit space, the model enriches the side information of the users and items. At last, we conduct comparative experiments on two public data sets, Movielens-100K and Movielens-1M. Experiment results express that the prediction accuracy of this model is better than other baselines in the task of predicting scores. In addition, these results also show that UISVD++ can effectively alleviate the cold start situation.
By allowing users to erase their data's impact on federated learning models, federated unlearning protects users' right to be forgotten and data privacy. Despite a burgeoning body of research on federated unlearning's technical feasibility, there is a paucity of literature investigating the considerations behind users' requests for data revocation. This paper proposes a non-cooperative game framework to study users' data revocation strategies in federated unlearning. We prove the existence of a Nash equilibrium. However, users' best response strategies are coupled via model performance and unlearning costs, which makes the equilibrium computation challenging. We obtain the Nash equilibrium by establishing its equivalence with a much simpler auxiliary optimization problem. We also summarize users' multi-dimensional attributes into a single-dimensional metric and derive the closed-form characterization of an equilibrium, when users' unlearning costs are negligible. Moreover, we compare the cases of allowing and forbidding partial data revocation in federated unlearning. Interestingly, the results reveal that allowing partial revocation does not necessarily increase users' data contributions or payoffs due to the game structure. Additionally, we demonstrate that positive externalities may exist between users' data revocation decisions when users incur unlearning costs, while this is not the case when their unlearning costs are negligible.
Data-driven machine learning approaches are being increasingly used to solve partial differential equations (PDEs). They have shown particularly striking successes when training an operator, which takes as input a PDE in some family, and outputs its solution. However, the architectural design space, especially given structural knowledge of the PDE family of interest, is still poorly understood. We seek to remedy this gap by studying the benefits of weight-tied neural network architectures for steady-state PDEs. To achieve this, we first demonstrate that the solution of most steady-state PDEs can be expressed as a fixed point of a non-linear operator. Motivated by this observation, we propose FNO-DEQ, a deep equilibrium variant of the FNO architecture that directly solves for the solution of a steady-state PDE as the infinite-depth fixed point of an implicit operator layer using a black-box root solver and differentiates analytically through this fixed point resulting in $\mathcal{O}(1)$ training memory. Our experiments indicate that FNO-DEQ-based architectures outperform FNO-based baselines with $4\times$ the number of parameters in predicting the solution to steady-state PDEs such as Darcy Flow and steady-state incompressible Navier-Stokes. Finally, we show FNO-DEQ is more robust when trained with datasets with more noisy observations than the FNO-based baselines, demonstrating the benefits of using appropriate inductive biases in architectural design for different neural network based PDE solvers. Further, we show a universal approximation result that demonstrates that FNO-DEQ can approximate the solution to any steady-state PDE that can be written as a fixed point equation.
Dataset distillation aims to generate a smaller but representative subset from a large dataset, which allows a model to be trained efficiently, meanwhile evaluating on the original testing data distribution to achieve decent performance. Many prior works have aimed to align with diverse aspects of the original datasets, such as matching the training weight trajectories, gradient, feature/BatchNorm distributions, etc. In this work, we show how to distill various large-scale datasets such as full ImageNet-1K/21K under a conventional input resolution of 224$\times$224 to achieve the best accuracy over all previous approaches, including SRe$^2$L, TESLA and MTT. To achieve this, we introduce a simple yet effective ${\bf C}$urriculum ${\bf D}$ata ${\bf A}$ugmentation ($\texttt{CDA}$) during data synthesis that obtains the accuracy on large-scale ImageNet-1K and 21K with 63.2% under IPC (Images Per Class) 50 and 36.1% under IPC 20, respectively. Finally, we show that, by integrating all our enhancements together, the proposed model beats the current state-of-the-art by more than 4% Top-1 accuracy on ImageNet-1K/21K and for the first time, reduces the gap to its full-data training counterpart to less than absolute 15%. Moreover, this work represents the inaugural success in dataset distillation on larger-scale ImageNet-21K under the standard 224$\times$224 resolution. Our code and distilled ImageNet-21K dataset of 20 IPC, 2K recovery budget are available at //github.com/VILA-Lab/SRe2L/tree/main/CDA.
We extend JAX with the capability to automatically differentiate higher-order functions (functionals and operators). By representing functions as a generalization of arrays, we seamlessly use JAX's existing primitive system to implement higher-order functions. We present a set of primitive operators that serve as foundational building blocks for constructing several key types of functionals. For every introduced primitive operator, we derive and implement both linearization and transposition rules, aligning with JAX's internal protocols for forward and reverse mode automatic differentiation. This enhancement allows for functional differentiation in the same syntax traditionally use for functions. The resulting functional gradients are themselves functions ready to be invoked in python. We showcase this tool's efficacy and simplicity through applications where functional derivatives are indispensable. The source code of this work is released at //github.com/sail-sg/autofd .
Causality can be described in terms of a structural causal model (SCM) that carries information on the variables of interest and their mechanistic relations. For most processes of interest the underlying SCM will only be partially observable, thus causal inference tries to leverage any exposed information. Graph neural networks (GNN) as universal approximators on structured input pose a viable candidate for causal learning, suggesting a tighter integration with SCM. To this effect we present a theoretical analysis from first principles that establishes a novel connection between GNN and SCM while providing an extended view on general neural-causal models. We then establish a new model class for GNN-based causal inference that is necessary and sufficient for causal effect identification. Our empirical illustration on simulations and standard benchmarks validate our theoretical proofs.
It is always well believed that modeling relationships between objects would be helpful for representing and eventually describing an image. Nevertheless, there has not been evidence in support of the idea on image description generation. In this paper, we introduce a new design to explore the connections between objects for image captioning under the umbrella of attention-based encoder-decoder framework. Specifically, we present Graph Convolutional Networks plus Long Short-Term Memory (dubbed as GCN-LSTM) architecture that novelly integrates both semantic and spatial object relationships into image encoder. Technically, we build graphs over the detected objects in an image based on their spatial and semantic connections. The representations of each region proposed on objects are then refined by leveraging graph structure through GCN. With the learnt region-level features, our GCN-LSTM capitalizes on LSTM-based captioning framework with attention mechanism for sentence generation. Extensive experiments are conducted on COCO image captioning dataset, and superior results are reported when comparing to state-of-the-art approaches. More remarkably, GCN-LSTM increases CIDEr-D performance from 120.1% to 128.7% on COCO testing set.
As a new classification platform, deep learning has recently received increasing attention from researchers and has been successfully applied to many domains. In some domains, like bioinformatics and robotics, it is very difficult to construct a large-scale well-annotated dataset due to the expense of data acquisition and costly annotation, which limits its development. Transfer learning relaxes the hypothesis that the training data must be independent and identically distributed (i.i.d.) with the test data, which motivates us to use transfer learning to solve the problem of insufficient training data. This survey focuses on reviewing the current researches of transfer learning by using deep neural network and its applications. We defined deep transfer learning, category and review the recent research works based on the techniques used in deep transfer learning.
注冊地址： 北京市海淀區羊坊店路18號2幢3層301-191