In Semi-supervised learning(SSL), we always accept cluster assumption, assuming features in different high-density regions belong to other categories. However, it is always ignored by existing algorithms and needs mathematical explanations. This paper first proposes a theorem to statistically explain cluster assumption and prove that the probability density can significantly help to use the prior fully. A Probability-Density-Aware Measure(PM) is proposed based on the theorem to discern the similarity between neighbor points. The PM is deployed to improve Label Propagation and a new pseudo-labeling algorithm, the Probability-Density-Aware Label Propagation(PMLP), is proposed. We also prove that traditional first-order similarity pseudo-labeling could be viewed as a particular case of PMLP, which provides a comprehensive theoretical understanding of PMLP's superior performance. Extensive experiments demonstrate that PMLP achieves outstanding performance compared with other recent methods.
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TimeCMA: Towards LLM-Empowered Multivariate Time Series Forecasting via Cross-Modality Alignment
PDF ↗Multivariate time series forecasting (MTSF) aims to learn temporal dynamics among variables to forecast future time series. Existing statistical and deep learning-based methods suffer from limited learnable parameters and small-scale training data. Recently, large language models (LLMs) combining time series with textual prompts have achieved promising performance in MTSF. However, we discovered that current LLM-based solutions fall short in learning disentangled embeddings. We introduce TimeCMA, an intuitive yet effective framework for MTSF via cross-modality alignment. Specifically, we present a dual-modality encoding with two branches: the time series encoding branch extracts disentangled yet weak time series embeddings, and the LLM-empowered encoding branch wraps the same time series with text as prompts to obtain entangled yet robust prompt embeddings. As a result, such a cross-modality alignment retrieves both disentangled and robust time series embeddings, ``the best of two worlds'', from the prompt embeddings based on time series and prompt modality similarities. As another key design, to reduce the computational costs from time series with their length textual prompts, we design an effective prompt to encourage the most essential temporal information to be encapsulated in the last token: only the last token is passed to downstream prediction. We further store the last token embeddings to accelerate inference speed. Extensive experiments on eight real datasets demonstrate that TimeCMA outperforms state-of-the-arts.
Identifying the Markov properties or conditional independencies of a collection of random variables is a fundamental task in statistics for modeling and inference. Existing approaches often learn the structure of a probabilistic graph, which encodes these dependencies, by assuming that the variables follow a distribution with a simple parametric form. Moreover, the computational cost of many algorithms scales poorly for high-dimensional distributions, as they need to estimate all the edges in the graph simultaneously. In this work, we propose a scalable algorithm to infer the conditional independence relationships of each variable by exploiting the local Markov property. The proposed method, named Localized Sparsity Identification for Non-Gaussian Distributions (L-SING), estimates the graph by using flexible classes of transport maps to represent the conditional distribution for each variable. We show that L-SING includes existing approaches, such as neighborhood selection with Lasso, as a special case. We demonstrate the effectiveness of our algorithm in both Gaussian and non-Gaussian settings by comparing it to existing methods. Lastly, we show the scalability of the proposed approach by applying it to high-dimensional non-Gaussian examples, including a biological dataset with more than 150 variables.
Diffusion models have shown promising ability in generating high-quality time series (TS) data. Despite the initial success, existing works mostly focus on the authenticity of data at the individual level, but pay less attention to preserving the population-level properties on the entire dataset. Such population-level properties include value distributions for each dimension and distributions of certain functional dependencies (e.g., cross-correlation, CC) between different dimensions. For instance, when generating house energy consumption TS data, the value distributions of the outside temperature and the kitchen temperature should be preserved, as well as the distribution of CC between them. Preserving such TS population-level properties is critical in maintaining the statistical insights of the datasets, mitigating model bias, and augmenting downstream tasks like TS prediction. Yet, it is often overlooked by existing models. Hence, data generated by existing models often bear distribution shifts from the original data. We propose Population-aware Diffusion for Time Series (PaD-TS), a new TS generation model that better preserves the population-level properties. The key novelties of PaD-TS include 1) a new training method explicitly incorporating TS population-level property preservation, and 2) a new dual-channel encoder model architecture that better captures the TS data structure. Empirical results in major benchmark datasets show that PaD-TS can improve the average CC distribution shift score between real and synthetic data by 5.9x while maintaining a performance comparable to state-of-the-art models on individual-level authenticity.
The convergence behavior of Stochastic Gradient Descent (SGD) crucially depends on the stepsize configuration. When using a constant stepsize, the SGD iterates form a Markov chain, enjoying fast convergence during the initial transient phase. However, when reaching stationarity, the iterates oscillate around the optimum without making further progress. In this paper, we study the convergence diagnostics for SGD with constant stepsize, aiming to develop an effective dynamic stepsize scheme. We propose a novel coupling-based convergence diagnostic procedure, which monitors the distance of two coupled SGD iterates for stationarity detection. Our diagnostic statistic is simple and is shown to track the transition from transience stationarity theoretically. We conduct extensive numerical experiments and compare our method against various existing approaches. Our proposed coupling-based stepsize scheme is observed to achieve superior performance across a diverse set of convex and non-convex problems. Moreover, our results demonstrate the robustness of our approach to a wide range of hyperparameters.
Noisy labels are both inevitable and problematic in machine learning methods, as they negatively impact models' generalization ability by causing overfitting. In the context of learning with noise, the transition matrix plays a crucial role in the design of statistically consistent algorithms. However, the transition matrix is often considered unidentifiable. One strand of methods typically addresses this problem by assuming that the transition matrix is instance-independent; that is, the probability of mislabeling a particular instance is not influenced by its characteristics or attributes. This assumption is clearly invalid in complex real-world scenarios. To better understand the transition relationship and relax this assumption, we propose to study the data generation process of noisy labels from a causal perspective. We discover that an unobservable latent variable can affect either the instance itself, the label annotation procedure, or both, which complicates the identification of the transition matrix. To address various scenarios, we have unified these observations within a new causal graph. In this graph, the input instance is divided into a noise-resistant component and a noise-sensitive component based on whether they are affected by the latent variable. These two components contribute to identifying the “causal transition matrix”, which approximates the true transition matrix with theoretical guarantee. In line with this, we have designed a novel training framework that explicitly models this causal relationship and, as a result, achieves a more accurate model for inferring the clean label.
Clustering ensemble has been a popular research topic in data science due to its ability to improve the robustness of the single clustering method. Many clustering ensemble methods have been proposed, most of which can be categorized into clustering-view and sample-view methods. The clustering-view method is generally efficient, but it could be affected by the unreliability that existed in base clustering results. The sample-view method shows good performance, while the construction of the pairwise sample relation is time-consuming. In this paper, the clustering ensemble is formulated as a k-HyperEdge Medoids discovery problem and a clustering ensemble method based on k-HyperEdge Medoids that considers the characteristics of the above two types of clustering ensemble methods is proposed. In the method, a set of hyperedges is selected from the clustering view efficiently, then the hyperedges are diffused and adjusted from the sample view guided by a hyperedge loss function to construct an effective k-HyperEdge Medoid set. The loss function is mainly reduced by assigning samples to the hyperedge with the highest degree of belonging. Theoretical analyses show that the solution can approximate the optimal, the assignment method can gradually reduce the loss function, and the estimation of the belonging degree is statistically reasonable. Experiments on artificial data show the working mechanism of the proposed method. The convergence of the method is verified by experimental analysis of twenty data sets. The effectiveness and efficiency of the proposed method are also verified on these data, with nine representative clustering ensemble algorithms as reference.
We consider the finite-horizon offline reinforcement learning (RL) setting, and are motivated by the challenge of learning the policy at any step h in dynamic programming (DP) algorithms. To learn this, it is sufficient to evaluate the treatment effect of deviating from the behavioral policy at step h after having optimized the policy for all future steps. Since the policy at any step can affect next-state distributions, the related distributional shift challenges can make this problem far more statistically hard than estimating such treatment effects in the stochastic contextual bandit setting. However, the hardness of many real-world RL instances lies between the two regimes. We develop a flexible and general method called selective uncertainty propagation for confidence interval construction that adapts to the hardness of the associated distribution shift challenges. We show benefits of our approach on toy environments and demonstrate the benefits of these techniques for offline policy learning.
Gradient Descent (GD) and Conjugate Gradient (CG) methods are among the most effective iterative algorithms for solving unconstrained optimization problems, particularly in machine learning and statistical modeling, where they are employed to minimize cost functions. In these algorithms, tunable parameters, such as step sizes or conjugate parameters, play a crucial role in determining key performance metrics, like runtime and solution quality. In this work, we introduce a framework that models algorithm selection as a statistical learning problem, and thus learning complexity can be estimated by the pseudo-dimension of the algorithm group. We first propose a new cost measure for unconstrained optimization algorithms, inspired by the concept of primal-dual integral in mixed-integer linear programming. Based on the new cost measure, we derive an improved upper bound for the pseudo-dimension of gradient descent algorithm group by discretizing the set of step size configurations. Moreover, we generalize our findings from gradient descent algorithm to the conjugate gradient algorithm group for the first time, and prove the existence a learning algorithm capable of probabilistically identifying the optimal algorithm with a sufficiently large sample size.
CUQDS: Conformal Uncertainty Quantification Under Distribution Shift for Trajectory Prediction
PDF ↗Trajectory prediction models that can infer both future trajectories and their associated uncertainties of the target vehicles is crucial for safe and robust navigation and path planning of autonomous vehicles. However, the majority of existing trajectory prediction models have neither considered reducing the uncertainty as one objective during the training stage nor provided reliable uncertainty quantification during inference stage, especially under potential distribution shift. Therefore, in this paper, we propose the Conformal Uncertainty Quantification under Distribution Shift framework, CUQDS, to quantify the uncertainty of the predicted trajectories of existing trajectory prediction models under potential data distribution shift, while improving the prediction accuracy of the models and reducing the estimated uncertainty during the training stage. Specifically, CUQDS includes 1) a learning-based Gaussian process regression module that models the output distribution of the base model (any existing trajectory prediction neural networks) and reduces the estimated uncertainty by an additional loss term, and 2) a statistical-based Conformal P control module to calibrate the estimated uncertainty from the Gaussian process regression module in an online setting under potential distribution shift between training and testing data. Experimental results on various state-of-the-art methods using benchmark motion forecasting datasets demonstrate the effectiveness of our proposed design.
Federated Learning (FL) is a distributed approach that enables collaborative model training while safeguarding client data privacy. Nevertheless, FL encounters difficulties due to statistical heterogeneity from the varied data distributions across numerous clients, which can affect overall efficiency and performance. Existing state-of-the-art FL methods often concentrate on optimizing interactions between clients, neglecting the potential insights from individual clients during training. Additionally, these approaches generally assume that every period of training has an equal impact on the final model's performance. To address these issues, this paper introduces a novel method, PA3Fed, which conducts period-aware adaptive aggregation for improved federated learning. The key idea is to identify the most critical periods, i.e., those with the highest information content and entropy, where we leverages each client's own performance variations during training for adaptive aggregation. Furthermore, because it operates independently of inter-client optimization approaches, it can be easily incorporated into other baselines for improved performance. Experimental results show that our method improves accuracy by up to 15% and significantly enhances stability.
FedAA: A Reinforcement Learning Perspective on Adaptive Aggregation for Fair and Robust Federated Learning
PDF ↗Federated Learning (FL) has emerged as a promising approach for privacy-preserving model training across decentralized devices. However, it faces challenges such as statistical heterogeneity and susceptibility to adversarial attacks, which can impact model robustness and fairness. Personalized FL attempts to provide some relief by customizing models for individual clients. However, it falls short in addressing server-side aggregation vulnerabilities. We introduce a novel method called FedAA, which optimizes client contributions via Adaptive Aggregation to enhance model robustness against malicious clients and ensure fairness across participants in non-identically distributed settings. To achieve this goal, we propose an approach involving a Deep Deterministic Policy Gradient-based algorithm for continuous control of aggregation weights, an innovative client selection method based on model parameter distances, and a reward mechanism guided by validation set performance. Empirically, extensive experiments demonstrate that, in terms of robustness, FedAA outperforms the state-of-the-art methods, while maintaining comparable levels of fairness, offering a promising solution to build resilient and fair federated systems.
Traditional Federated Learning (FL) necessitates numerous rounds of communication between the server and clients, posing significant challenges including high communication costs, connection drop risks and susceptibility to privacy attacks. One-shot FL has become a compelling learning paradigm to overcome above drawbacks by enabling the training of a global server model via a single communication round. However, existing one-shot FL methods suffer from expensive computation cost on the server or clients and cannot deal with non-IID (Independent and Identically Distributed) data stably and effectively. To address these challenges, this paper proposes FedCGS, a novel Federated learning algorithm that Capture Global feature Statistics leveraging pre-trained models. With global feature statistics, we achieve training-free and heterogeneity-resistant one-shot FL. Furthermore, we expand its application to personalization scenario, where clients only need execute one extra communication round with server to download global statistics. Extensive experimental results demonstrate the effectiveness of our methods across diverse data-heterogeneity settings.
Conditional demographic parity (CDP) is a measure of the demographic parity of a predictive model or decision process when conditioning on an additional feature or set of features. Many algorithmic fairness techniques exist to target demographic parity, but CDP is much harder to achieve, particularly when the conditioning variable has many levels and/or when the model outputs are continuous. The problem of auditing and enforcing CDP is understudied in the literature. In light of this, we propose novel measures of conditional demographic disparity (CDD) which rely on statistical distances borrowed from the optimal transport literature. We further design and evaluate regularization-based approaches based on these CDD measures. Our methods, FairBiT and FairLeap, allow us to target conditional demographic parity even when the conditioning variable has many levels. When model outputs are continuous, our methods target full equality of the conditional distributions, unlike other methods that only consider first moments or related proxy quantities. We validate our approaches on real-world datasets.
Recent advancements in Zero-shot Neural Architecture Search (NAS) highlight the ability of zero-cost proxies in identifying superior architecture. However, we identify a critical issue with current zero-cost proxies: they aggregate node-wise zero-cost statistics without considering that not all nodes in a neural network equally impact performance estimation. Our observations reveal that node-wise zero-cost statistics significantly vary in their contributions to performance, with each node exhibiting a degree of uncertainty. Based on this insight, we introduce a novel method called Parametric Zero-Cost Proxies (ParZC) framework to enhance the adaptability of zero-cost proxies through parameterization. To address the node indiscrimination, we propose a Mixer Architecture with Bayesian Network (MABN) to explore the node-wise zero-cost statistics and estimate node-specific uncertainty. Moreover, we propose DiffKendall as a loss function to improve ranking consistency. Comprehensive experiments on NAS-Bench-101, 201, and NDS demonstrate the superiority of our proposed ParZC compared to existing zero-shot NAS methods. Additionally, we demonstrate the versatility and adaptability of ParZC on Vision Transformer search space.
Confidence calibration of classification models is a technique to estimate the true posterior probability of the predicted class, which is critical for ensuring reliable decision-making in practical applications. Existing confidence calibration methods mostly use statistical techniques to estimate the calibration curve from data or fit a user-defined calibration function, but often overlook fully mining and utilizing the prior distribution behind the calibration curve. However, a well-informed prior distribution can provide valuable insights beyond the empirical data under the limited data or low-density regions of confidence scores. To fill this gap, this paper proposes a new method that integrates the prior distribution behind the calibration curve with empirical data to estimate a continuous calibration curve, which is realized by modeling the sampling process of calibration data as a binomial process and maximizing the likelihood function of the binomial process. We prove that the calibration curve estimating method is Lipschitz continuous with respect to data distribution and requires smaller sample sizes than histogram binning. Also, a new calibration metric has been designed, leveraging the estimated calibration curve to estimate the true calibration error, and it has been proven to be a consistent calibration measure. Furthermore, realistic calibration datasets can be generated by the binomial process modeling from a preset true calibration curve and confidence score distribution, which can serve as a benchmark to measure and compare the discrepancy between existing calibration metrics and the true calibration error. The effectiveness of our calibration method and metric are verified in real-world and simulated data. We believe our exploration of integrating prior distributions with empirical data will guide the development of better-calibrated models, contributing to trustworthy AI.
Learning with noisy labels (LNL) methods have enabled the deployment of machine learning systems with imperfectly labeled data. However, these methods often struggle to identify noise in the presence of long-tailed (LT) class distributions, where the memorization effect becomes class-dependent. Conversely, LT methods are suboptimal under label noise, as it hinders access to accurate label frequency statistics. This study aims to address the long-tailed noisy data by bridging the methodological gap between LNL and LT approaches. We propose a direct solution, termed Robust Logit Adjustment, which estimates ground-truth labels through label refurbishment, thereby mitigating the impact of label noise. Simultaneously, our method incorporates the distribution of training-time corrected target labels into the LT method logit adjustment, providing class-rebalanced supervision. Extensive experiments on both synthetic and real-world long-tailed noisy datasets demonstrate the superior performance of our method.
This paper proposes a method for measuring conditional feature importance via generative modeling. In explainable artificial intelligence (XAI), conditional feature importance assesses the impact of a feature on a prediction model's performance given the information of other features. Model-agnostic post hoc methods to do so typically evaluate changes in the predictive performance under on-manifold feature value manipulations. Such procedures require creating feature values that respect conditional feature distributions, which can be challenging in practice. Recent advancements in generative modeling can facilitate this. For tabular data, which may consist of both categorical and continuous features, the adversarial random forest (ARF) stands out as a generative model that can generate on-manifold data points without requiring intensive tuning efforts or computational resources, making it a promising candidate model for subroutines in XAI methods. This paper proposes cARFi (conditional ARF feature importance), a method for measuring conditional feature importance through feature values sampled from ARF-estimated conditional distributions. cARFi requires only little tuning to yield robust importance scores that can flexibly adapt for conditional or marginal notions of feature importance, including straightforward extensions to condition on feature subsets and allows for inferring the significance of feature importances through statistical tests.
Exponential-family harmoniums (EFHs) generalize the restricted Boltzmann machine beyond Bernoulli random variables to other exponential families. Here we show how to extend the EFH beyond standard exponential families (Poisson, Gaussian, etc.), by allowing the sufficient statistics for the hidden units to be arbitrary functions of the observed data, parameterized by deep neural networks. This rules out the standard sampling scheme, block Gibbs sampling, so we replace it with a form of Langevin dynamics within Gibbs, inspired by a recent method for training Gaussian restricted Boltzmann machines (GRBMs). With Gibbs-Langevin, the GRBM can successfully model small datasets like MNIST and CelebA-32, but struggles with CIFAR-10, and cannot scale to larger images because it lacks convolutions. In contrast, our neural-network EFHs (NN-EFHs) generate high-quality samples from CIFAR-10 and scale well to CelebA-HQ. On these datasets, the NN-EFH achieves FID scores that are 25--50% lower than a standard energy-based model with a similar neural-network architecture and the same number of parameters; and competitive with noise-conditional score networks, which utilize more complex neural networks (U-nets) and require considerably more sampling steps.
Existing learning-from-crowds methods aim to design proper aggregation strategies to infer the unknown true labels from noisy labels provided by crowdsourcing. They treat the ground truth as hidden variables and use statistical or deep learning based worker behavior models to infer the ground truth. However, worker behavior models that rely on ground truth hidden variables overlook workers' behavior at the item feature level, leading to imprecise characterizations and negatively impacting the quality of learning-from-crowds. This paper proposes a new paradigm of multi-task supervised learning-from-crowds, which eliminates the need for modeling of items's ground truth in worker behavior models. Within this paradigm, we propose a worker behavior model at the item feature level called Mixture of Experts based Multi-task Supervised Learning-from-Crowds (MMLC), then, two aggregation strategies are proposed within MMLC. The first strategy, named MMLC-owf, utilizes clustering methods in the worker spectral space to identify the projection vector of the oracle worker. Subsequently, the labels generated based on this vector are regarded as the items's ground truth The second strategy, called MMLC-df, employs the MMLC model to fill the crowdsourced data, which can enhance the effectiveness of existing aggregation strategies . Experimental results demonstrate that MMLC-owf outperforms state-of-the-art methods and MMLC-df enhances the quality of existing learning-from-crowds methods.