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Label distribution learning (LDL) differs from multi-label learning which aims at representing the polysemy of instances by transforming single-label values into descriptive degrees. Unfortunately, the feature space of the label distribution dataset is affected by human factors and the inductive bias of the feature extractor causing uncertainty in the feature space. Especially, for datasets with small-scale feature spaces (the feature space dimension $\approx$ the label space), the existing LDL algorithms do not perform well. To address this issue, we seek to model the uncertainty augmentation of the feature space to alleviate the problem in LDL tasks. Specifically, we start with augmenting each feature value in the feature vector of a sample into a vector (sampling on a Gaussian distribution function). Which, the variance parameter of the Gaussian distribution function is learned by using a sub-network, and the mean parameter is filled by this feature value. Then, each feature vector is augmented to a matrix which is fed into a mixer with local attention (\textit{TabMixer}) to extract the latent feature. Finally, the latent feature is squeezed to yield an accurate label distribution via a squeezed network. Extensive experiments verify that our proposed algorithm can be competitive compared to other LDL algorithms on several benchmarks.

Recovering linear subspaces from data is a fundamental and important task in statistics and machine learning. Motivated by heterogeneity in Federated Learning settings, we study a basic formulation of this problem: the principal component analysis (PCA), with a focus on dealing with irregular noise. Our data come from $n$ users with user $i$ contributing data samples from a $d$-dimensional distribution with mean $\mu_i$. Our goal is to recover the linear subspace shared by $\mu_1,\ldots,\mu_n$ using the data points from all users, where every data point from user $i$ is formed by adding an independent mean-zero noise vector to $\mu_i$. If we only have one data point from every user, subspace recovery is information-theoretically impossible when the covariance matrices of the noise vectors can be non-spherical, necessitating additional restrictive assumptions in previous work. We avoid these assumptions by leveraging at least two data points from each user, which allows us to design an efficiently-computable estimator under non-spherical and user-dependent noise. We prove an upper bound for the estimation error of our estimator in general scenarios where the number of data points and amount of noise can vary across users, and prove an information-theoretic error lower bound that not only matches the upper bound up to a constant factor, but also holds even for spherical Gaussian noise. This implies that our estimator does not introduce additional estimation error (up to a constant factor) due to irregularity in the noise. We show additional results for a linear regression problem in a similar setup.

In this paper, we establish the global optimality and convergence rate of an off-policy actor critic algorithm in the tabular setting without using density ratio to correct the discrepancy between the state distribution of the behavior policy and that of the target policy. Our work goes beyond existing works on the optimality of policy gradient methods in that existing works use the exact policy gradient for updating the policy parameters while we use an approximate and stochastic update step. Our update step is not a gradient update because we do not use a density ratio to correct the state distribution, which aligns well with what practitioners do. Our update is approximate because we use a learned critic instead of the true value function. Our update is stochastic because at each step the update is done for only the current state action pair. Moreover, we remove several restrictive assumptions from existing works in our analysis. Central to our work is the finite sample analysis of a generic stochastic approximation algorithm with time-inhomogeneous update operators on time-inhomogeneous Markov chains, based on its uniform contraction properties.

In randomized experiments and observational studies, weighting methods are often used to generalize and transport treatment effect estimates to a target population. Traditional methods construct the weights by separately modeling the treatment assignment and study selection probabilities and then multiplying functions (e.g., inverses) of their estimates. However, these estimated multiplicative weights may not produce adequate covariate balance and can be highly variable, resulting in biased and unstable estimators, especially when there is limited covariate overlap across populations or treatment groups. To address these limitations, we propose a general weighting approach that weights each treatment group towards the target population in a single step. We present a framework and provide a justification for this one-step approach in terms of generic probability distributions. We show a formal connection between our method and inverse probability and inverse odds weighting. By construction, the proposed approach balances covariates and produces stable estimators. We show that our estimator for the target average treatment effect is consistent, asymptotically Normal, multiply robust, and semiparametrically efficient. We demonstrate the performance of this approach using a simulation study and a randomized case study on the effects of physician racial diversity on preventive healthcare utilization among Black men in California.

Federated learning (FedL) has emerged as a popular technique for distributing model training over a set of wireless devices, via iterative local updates (at devices) and global aggregations (at the server). In this paper, we develop parallel successive learning (PSL), which expands the FedL architecture along three dimensions: (i) Network, allowing decentralized cooperation among the devices via device-to-device (D2D) communications. (ii) Heterogeneity, interpreted at three levels: (ii-a) Learning: PSL considers heterogeneous number of stochastic gradient descent iterations with different mini-batch sizes at the devices; (ii-b) Data: PSL presumes a dynamic environment with data arrival and departure, where the distributions of local datasets evolve over time, captured via a new metric for model/concept drift. (ii-c) Device: PSL considers devices with different computation and communication capabilities. (iii) Proximity, where devices have different distances to each other and the access point. PSL considers the realistic scenario where global aggregations are conducted with idle times in-between them for resource efficiency improvements, and incorporates data dispersion and model dispersion with local model condensation into FedL. Our analysis sheds light on the notion of cold vs. warmed up models, and model inertia in distributed machine learning. We then propose network-aware dynamic model tracking to optimize the model learning vs. resource efficiency tradeoff, which we show is an NP-hard signomial programming problem. We finally solve this problem through proposing a general optimization solver. Our numerical results reveal new findings on the interdependencies between the idle times in-between the global aggregations, model/concept drift, and D2D cooperation configuration.

Online imitation learning is the problem of how best to mimic expert demonstrations, given access to the environment or an accurate simulator. Prior work has shown that in the infinite sample regime, exact moment matching achieves value equivalence to the expert policy. However, in the finite sample regime, even if one has no optimization error, empirical variance can lead to a performance gap that scales with $H^2 / N$ for behavioral cloning and $H / \sqrt{N}$ for online moment matching, where $H$ is the horizon and $N$ is the size of the expert dataset. We introduce the technique of replay estimation to reduce this empirical variance: by repeatedly executing cached expert actions in a stochastic simulator, we compute a smoother expert visitation distribution estimate to match. In the presence of general function approximation, we prove a meta theorem reducing the performance gap of our approach to the parameter estimation error for offline classification (i.e. learning the expert policy). In the tabular setting or with linear function approximation, our meta theorem shows that the performance gap incurred by our approach achieves the optimal $\widetilde{O} \left( \min({H^{3/2}} / {N}, {H} / {\sqrt{N}} \right)$ dependency, under significantly weaker assumptions compared to prior work. We implement multiple instantiations of our approach on several continuous control tasks and find that we are able to significantly improve policy performance across a variety of dataset sizes.

A difficulty in MSE estimation occurs because we do not specify a full distribution for the survey weights. This obfuscates the use of fully parametric bootstrap procedures. To overcome this challenge, we develop a novel MSE estimator. We estimate the leading term in the MSE, which is the MSE of the best predictor (constructed with the true parameters), using the same simulated samples used to construct the basic predictor. We then exploit the asymptotic normal distribution of the parameter estimators to estimate the second term in the MSE, which reflects variability in the estimated parameters. We incorporate a correction for the bias of the estimator of the leading term without the use of computationally intensive double-bootstrap procedures. We further develop calibrated prediction intervals that rely less on normal theory than standard prediction intervals. We empirically demonstrate the validity of the proposed procedures through extensive simulation studies. We apply the methods to predict several functions of sheet and rill erosion for Iowa counties using data from a complex agricultural survey.

We present prompt distribution learning for effectively adapting a pre-trained vision-language model to address downstream recognition tasks. Our method not only learns low-bias prompts from a few samples but also captures the distribution of diverse prompts to handle the varying visual representations. In this way, we provide high-quality task-related content for facilitating recognition. This prompt distribution learning is realized by an efficient approach that learns the output embeddings of prompts instead of the input embeddings. Thus, we can employ a Gaussian distribution to model them effectively and derive a surrogate loss for efficient training. Extensive experiments on 12 datasets demonstrate that our method consistently and significantly outperforms existing methods. For example, with 1 sample per category, it relatively improves the average result by 9.1% compared to human-crafted prompts.

Graph Convolutional Networks (GCNs) have been widely applied in various fields due to their significant power on processing graph-structured data. Typical GCN and its variants work under a homophily assumption (i.e., nodes with same class are prone to connect to each other), while ignoring the heterophily which exists in many real-world networks (i.e., nodes with different classes tend to form edges). Existing methods deal with heterophily by mainly aggregating higher-order neighborhoods or combing the immediate representations, which leads to noise and irrelevant information in the result. But these methods did not change the propagation mechanism which works under homophily assumption (that is a fundamental part of GCNs). This makes it difficult to distinguish the representation of nodes from different classes. To address this problem, in this paper we design a novel propagation mechanism, which can automatically change the propagation and aggregation process according to homophily or heterophily between node pairs. To adaptively learn the propagation process, we introduce two measurements of homophily degree between node pairs, which is learned based on topological and attribute information, respectively. Then we incorporate the learnable homophily degree into the graph convolution framework, which is trained in an end-to-end schema, enabling it to go beyond the assumption of homophily. More importantly, we theoretically prove that our model can constrain the similarity of representations between nodes according to their homophily degree. Experiments on seven real-world datasets demonstrate that this new approach outperforms the state-of-the-art methods under heterophily or low homophily, and gains competitive performance under homophily.

Analyzing observational data from multiple sources can be useful for increasing statistical power to detect a treatment effect; however, practical constraints such as privacy considerations may restrict individual-level information sharing across data sets. This paper develops federated methods that only utilize summary-level information from heterogeneous data sets. Our federated methods provide doubly-robust point estimates of treatment effects as well as variance estimates. We derive the asymptotic distributions of our federated estimators, which are shown to be asymptotically equivalent to the corresponding estimators from the combined, individual-level data. We show that to achieve these properties, federated methods should be adjusted based on conditions such as whether models are correctly specified and stable across heterogeneous data sets.