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Miscellaneous Aspects of Machine Learning/Unsupervised and Semi-supervised Learning

Eduardo Laber, Lucas Murtinho

Internal measures that are used to assess the quality of a clustering usually take into account intra-group and/or inter-group criteria.There are many papers in the literature that propose algorithms with provable approximation guarantees for optimizing the former. However, the optimization of inter-group criteria is much less understood.Here, we contribute to the state-of-the-art of this literature by devising algorithms with provable guarantees for the maximization of two natural inter-group criteria, namely the minimum spacing and the minimum spanning tree spacing. The former is the minimum distance between points in different groups while the latter captures separability through the cost of the minimum spanning tree that connects all groups. We obtain results for both the unrestricted case, in which no constraint on the clusters is imposed, and for the constrained case where each group is required to have a minimum number of points. Our constraint is motivated by the fact that the popular Single-Linkage, which optimizes both criteria in the unrestricted case, produces clustering with many tiny groups.To complement our work, we present an empirical study with 10 real datasets that provides evidence that our methods work very well in practical settings.

Miscellaneous Aspects of Machine Learning/Online Learning, Active Learning and Bandits

Adam Block, Max Simchowitz, Russ Tedrake

The problem of piecewise affine (PWA) regression and planning is of foundational importance to the study of online learning, control, and robotics, where it provides a theoretically and empirically tractable setting to study systems undergoing sharp changes in the dynamics. Unfortunately, due to the discontinuities that arise when crossing into different ``pieces,'' learning in general sequential settings is impossible and practical algorithms are forced to resort to heuristic approaches. This paper builds on the recently developed smoothed online learning framework and provides the first algorithms for prediction and simulation in PWA systems whose regret is polynomial in all relevant problem parameters under a weak smoothness assumption; moreover, our algorithms are efficient in the number of calls to an optimization oracle. We further apply our results to the problems of one-step prediction and multi-step simulation regret in piecewise affine dynamical systems, where the learner is tasked with simulating trajectories and regret is measured in terms of the Wasserstein distance between simulated and true data. Along the way, we develop several technical tools of more general interest.

Theory/Miscellaneous Aspects of Machine Learning

Hossein Esfandiari, Amin Karbasi, Vahab Mirrokni, Grigoris Velegkas, Felix Zhou

We design replicable algorithms in the context of statistical clustering under the recently introduced notion of replicability from Impagliazzo et al. [2022]. According to this definition, a clustering algorithm is replicable if, with high probability, its output induces the exact same partition of the sample space after two executions on different inputs drawn from the same distribution, when its internal randomness is shared across the executions. We propose such algorithms for the statistical $k$-medians, statistical $k$-means, and statistical $k$-centers problems by utilizing approximation routines for their combinatorial counterparts in a black-box manner. In particular, we demonstrate a replicable $O(1)$-approximation algorithm for statistical Euclidean $k$-medians ($k$-means) with $\operatorname{poly}(d)$ sample complexity. We also describe an $O(1)$-approximation algorithm with an additional $O(1)$-additive error for statistical Euclidean $k$-centers, albeit with $\exp(d)$ sample complexity. In addition, we provide experiments on synthetic distributions in 2D using the $k$-means++ implementation from sklearn as a black-box that validate our theoretical results.

Miscellaneous Aspects of Machine Learning/Transfer, Multitask and Meta-learning

Qiong Wu, Wei Yu, Yiyi Zhou, Shubin Huang, Xiaoshuai Sun, Rongrong Ji

With ever increasing parameters and computation, vision-language pre-trained (VLP) models exhibit prohibitive expenditure in downstream task adaption. Recent endeavors mainly focus on parameter efficient transfer learning (PETL) for VLP models by only updating a small number of parameters. However, excessive computational overhead still plagues the application of VLPs. In this paper, we aim at parameter and computation efficient transfer learning (PCETL) for VLP models. In particular, PCETL not only needs to limit the number of trainable parameters in VLP models, but also to reduce the computational redundancy during inference, thus enabling a more efficient transfer. To approach this target, we propose a novel dynamic architecture skipping (DAS) approach towards effective PCETL. Instead of directly optimizing the intrinsic architectures of VLP models, DAS first observes the significances of their modules to downstream tasks via a reinforcement learning (RL) based process, and then skips the redundant ones with lightweight networks, i.e. adapters, according to the obtained rewards. In this case, the VLP model can well maintain the scale of trainable parameters while speeding up its inference on downstream tasks. To validate DAS, we apply it to two representative VLP models, namely ViLT and METER, and conduct extensive experiments on a bunch of VL tasks. The experimental results not only show the great advantages of DAS in reducing computational complexity, e.g. -11.97% FLOPs of METER on VQA2.0, but also confirm its competitiveness against existing PETL methods in terms of parameter scale and performance. Our source code is given in our appendix.

Miscellaneous Aspects of Machine Learning/Supervised Learning

Naoki Nishikawa, Yuichi Ike, Kenji Yamanishi

Machine learning for point clouds has been attracting much attention, with many applications in various fields, such as shape recognition and material science. For enhancing the accuracy of such machine learning methods, it is often effective to incorporate global topological features, which are typically extracted by persistent homology. In the calculation of persistent homology for a point cloud, we choose a filtration for the point cloud, an increasing sequence of spaces. Since the performance of machine learning methods combined with persistent homology is highly affected by the choice of a filtration, we need to tune it depending on data and tasks. In this paper, we propose a framework that learns a filtration adaptively with the use of neural networks. In order to make the resulting persistent homology isometry-invariant, we develop a neural network architecture with such invariance. Additionally, we show a theoretical result on a finite-dimensional approximation of filtration functions, which justifies the proposed network architecture. Experimental results demonstrated the efficacy of our framework in several classification tasks.

Miscellaneous Aspects of Machine Learning/Transfer, Multitask and Meta-learning

Dipam Goswami, Yuyang Liu, Bartłomiej Twardowski, Joost van de Weijer

Exemplar-free class-incremental learning (CIL) poses several challenges since it prohibits the rehearsal of data from previous tasks and thus suffers from catastrophic forgetting. Recent approaches to incrementally learning the classifier by freezing the feature extractor after the first task have gained much attention. In this paper, we explore prototypical networks for CIL, which generate new class prototypes using the frozen feature extractor and classify the features based on the Euclidean distance to the prototypes. In an analysis of the feature distributions of classes, we show that classification based on Euclidean metrics is successful for jointly trained features. However, when learning from non-stationary data, we observe that the Euclidean metric is suboptimal and that feature distributions are heterogeneous. To address this challenge, we revisit the anisotropic Mahalanobis distance for CIL. In addition, we empirically show that modeling the feature covariance relations is better than previous attempts at sampling features from normal distributions and training a linear classifier. Unlike existing methods, our approach generalizes to both many- and few-shot CIL settings, as well as to domain-incremental settings. Interestingly, without updating the backbone network, our method obtains state-of-the-art results on several standard continual learning benchmarks. Code is available at https://github.com/dipamgoswami/FeCAM.

Miscellaneous Aspects of Machine Learning/Causality

Dennis Frauen, Valentyn Melnychuk, Stefan Feuerriegel

Causal inference from observational data is crucial for many disciplines such as medicine and economics. However, sharp bounds for causal effects under relaxations of the unconfoundedness assumption (causal sensitivity analysis) are subject to ongoing research. So far, works with sharp bounds are restricted to fairly simple settings (e.g., a single binary treatment). In this paper, we propose a unified framework for causal sensitivity analysis under unobserved confounding in various settings. For this, we propose a flexible generalization of the marginal sensitivity model (MSM) and then derive sharp bounds for a large class of causal effects. This includes (conditional) average treatment effects, effects for mediation analysis and path analysis, and distributional effects. Furthermore, our sensitivity model is applicable to discrete, continuous, and time-varying treatments. It allows us to interpret the partial identification problem under unobserved confounding as a distribution shift in the latent confounders while evaluating the causal effect of interest. In the special case of a single binary treatment, our bounds for (conditional) average treatment effects coincide with recent optimality results for causal sensitivity analysis. Finally, we propose a scalable algorithm to estimate our sharp bounds from observational data.

Miscellaneous Aspects of Machine Learning/Everything Else

Yu Gui, Rina Barber, Cong Ma

Matrix completion aims to estimate missing entries in a data matrix, using the assumption of a low-complexity structure (e.g., low-rankness) so that imputation is possible. While many effective estimation algorithms exist in the literature, uncertainty quantification for this problem has proved to be challenging, and existing methods are extremely sensitive to model misspecification. In this work, we propose a distribution-free method for predictive inference in the matrix completion problem. Our method adapts the framework of conformal prediction, which provides prediction intervals with guaranteed distribution-free validity in the setting of regression, to the problem of matrix completion. Our resulting method, conformalized matrix completion (cmc), offers provable predictive coverage regardless of the accuracy of the low-rank model. Empirical results on simulated and real data demonstrate that cmc is robust to model misspecification while matching the performance of existing model-based methods when the model is correct.

Applications/Language, Speech and Dialog

Yinghao Aaron Li, Cong Han, Vinay Raghavan, Gavin Mischler, Nima Mesgarani

In this paper, we present StyleTTS 2, a text-to-speech (TTS) model that leverages style diffusion and adversarial training with large speech language models (SLMs) to achieve human-level TTS synthesis. StyleTTS 2 differs from its predecessor by modeling styles as a latent random variable through diffusion models to generate the most suitable style for the text without requiring reference speech, achieving efficient latent diffusion while benefiting from the diverse speech synthesis offered by diffusion models. Furthermore, we employ large pre-trained SLMs, such as WavLM, as discriminators with our novel differentiable duration modeling for end-to-end training, resulting in improved speech naturalness. StyleTTS 2 surpasses human recordings on the single-speaker LJSpeech dataset and matches it on the multispeaker VCTK dataset as judged by native English speakers. Moreover, when trained on the LibriTTS dataset, our model outperforms previous publicly available models for zero-shot speaker adaptation. This work achieves the first human-level TTS on both single and multispeaker datasets, showcasing the potential of style diffusion and adversarial training with large SLMs. The audio demos and source code are available at https://styletts2.github.io/.

Miscellaneous Aspects of Machine Learning/Causality

Xiangyu Sun, Oliver Schulte

A fundamental problem of causal discovery is cause-effect inference, to learn the correct causal direction between two random variables. Significant progress has been made through modelling the effect as a function of its cause and a noise term, which allows us to leverage assumptions about the generating function class. The recently introduced heteroscedastic location-scale noise functional models (LSNMs) combine expressive power with identifiability guarantees. LSNM model selection based on maximizing likelihood achieves state-of-the-art accuracy, when the noise distributions are correctly specified. However, through an extensive empirical evaluation, we demonstrate that the accuracy deteriorates sharply when the form of the noise distribution is misspecified by the user. Our analysis shows that the failure occurs mainly when the conditional variance in the anti-causal direction is smaller than that in the causal direction. As an alternative, we find that causal model selection through residual independence testing is much more robust to noise misspecification and misleading conditional variance.

Miscellaneous Aspects of Machine Learning/Transfer, Multitask and Meta-learning

Kaipeng Zheng, Huishuai Zhang, Weiran Huang

Few-shot learning aims to adapt models trained on the base dataset to novel tasks where the categories were not seen by the model before. This often leads to a relatively concentrated distribution of feature values across channels on novel classes, posing challenges in determining channel importance for novel tasks. Standard few-shot learning methods employ geometric similarity metrics such as cosine similarity and negative Euclidean distance to gauge the semantic relatedness between two features. However, features with high geometric similarities may carry distinct semantics, especially in the context of few-shot learning. In this paper, we demonstrate that the importance ranking of feature channels is a more reliable indicator for few-shot learning than geometric similarity metrics. We observe that replacing the geometric similarity metric with Kendall’s rank correlation only during inference is able to improve the performance of few-shot learning across a wide range of methods and datasets with different domains. Furthermore, we propose a carefully designed differentiable loss for meta-training to address the non-differentiability issue of Kendall’s rank correlation. By replacing geometric similarity with differentiable Kendall’s rank correlation, our method can integrate with numerous existing few-shot approaches and is ready for integrating with future state-of-the-art methods that rely on geometric similarity metrics. Extensive experiments validate the efficacy of the rank-correlation-based approach, showcasing a significant improvement in few-shot learning.

Miscellaneous Aspects of Machine Learning/General Machine Learning Techniques

Zhilin Zhao, Longbing Cao

Real-life data are often non-IID due to complex distributions and interactions, and the sensitivity to the distribution of samples can differ among learning models. Accordingly, a key question for any supervised or unsupervised model is whether the probability distributions of two given datasets can be considered identical. To address this question, we introduce R-divergence, designed to assess model-oriented distribution discrepancies. The core insight is that two distributions are likely identical if their optimal hypothesis yields the same expected risk for each distribution. To estimate the distribution discrepancy between two datasets, R-divergence learns a minimum hypothesis on the mixed data and then gauges the empirical risk difference between them. We evaluate the test power across various unsupervised and supervised tasks and find that R-divergence achieves state-of-the-art performance. To demonstrate the practicality of R-divergence, we employ R-divergence to train robust neural networks on samples with noisy labels.

Miscellaneous Aspects of Machine Learning/Causality

Shuai Li, Yingjie Zhang, Hongtu Zhu, Christina Wang, Hai Shu, Ziqi Chen, Zhuoran Sun, Yanfeng Yang

Conditional independence (CI) testing is a fundamental task in statistics and machine learning, but its effectiveness is hindered by the challenges posed by high-dimensional conditioning variables and limited data samples. This article introduces a novel testing approach to address these challenges and enhance control of the type I error while achieving high power under alternative hypotheses. The proposed approach incorporates a computationally efficient classifier-based conditional mutual information (CMI) estimator, capable of capturing intricate dependence structures among variables. To approximate a distribution encoding the null hypothesis, a $k$-nearest-neighbor local sampling strategy is employed. An important advantage of this approach is its ability to operate without assumptions about distribution forms or feature dependencies. Furthermore, it eliminates the need to derive asymptotic null distributions for the estimated CMI and avoids dataset splitting, making it particularly suitable for small datasets. The method presented in this article demonstrates asymptotic control of the type I error and consistency against all alternative hypotheses. Extensive analyses using both synthetic and real data highlight the computational efficiency of the proposed test. Moreover, it outperforms existing state-of-the-art methods in terms of type I and II errors, even in scenarios with high-dimensional conditioning sets. Additionally, the proposed approach exhibits robustness in the presence of heavy-tailed data.

Miscellaneous Aspects of Machine Learning/Online Learning, Active Learning and Bandits

Zhekai Du, Jingjing Li

Active Domain Adaptation (ADA) has emerged as an attractive technique for assisting domain adaptation by actively annotating a small subset of target samples. Most ADA methods focus on measuring the target representativeness beyond traditional active learning criteria to handle the domain shift problem, while leaving the uncertainty estimation to be performed by an uncalibrated deterministic model. In this work, we introduce a probabilistic framework that captures both data-level and prediction-level uncertainties beyond a point estimate. Specifically, we use variational inference to approximate the joint posterior distribution of latent representation and model prediction. The variational objective of labeled data can be formulated by a variational autoencoder and a latent diffusion classifier, and the objective of unlabeled data can be implemented in a knowledge distillation framework. We utilize adversarial learning to ensure an invariant latent space. The resulting diffusion classifier enables efficient sampling of all possible predictions for each individual to recover the predictive distribution. We then leverage a t-test-based criterion upon the sampling and select informative unlabeled target samples based on the p-value, which encodes both prediction variability and cross-category ambiguity. Experiments on both ADA and Source-Free ADA settings show that our method provides more calibrated predictions than previous ADA methods and achieves favorable performance on three domain adaptation datasets.

Miscellaneous Aspects of Machine Learning/Unsupervised and Semi-supervised Learning

Zhuo Huang, Li Shen, Jun Yu, Bo Han, Tongliang Liu

Semi-Supervised Learning (SSL) has been an effective way to leverage abundant unlabeled data with extremely scarce labeled data. However, most SSL methods are commonly based on instance-wise consistency between different data transformations. Therefore, the label guidance on labeled data is hard to be propagated to unlabeled data. Consequently, the learning process on labeled data is much faster than on unlabeled data which is likely to fall into a local minima that does not favor unlabeled data, leading to sub-optimal generalization performance. In this paper, we propose FlatMatch which minimizes a cross-sharpness measure to ensure consistent learning performance between the two datasets. Specifically, we increase the empirical risk on labeled data to obtain a worst-case model which is a failure case needing to be enhanced. Then, by leveraging the richness of unlabeled data, we penalize the prediction difference (i.e., cross-sharpness) between the worst-case model and the original model so that the learning direction is beneficial to generalization on unlabeled data. Therefore, we can calibrate the learning process without being limited to insufficient label information. As a result, the mismatched learning performance can be mitigated, further enabling the effective exploitation of unlabeled data and improving SSL performance. Through comprehensive validation, we show FlatMatch achieves state-of-the-art results in many SSL settings.

Miscellaneous Aspects of Machine Learning/General Machine Learning Techniques

Feiyang Kang, Hoang Anh Just, Anit Kumar Sahu, Ruoxi Jia

Traditionally, data selection has been studied in settings where all samples from prospective sources are fully revealed to a machine learning developer. However, in practical data exchange scenarios, data providers often reveal only a limited subset of samples before an acquisition decision is made. Recently, there have been efforts to fit scaling functions that predict model performance at any *size and data source composition* using the limited available samples. However, these scaling functions are usually black-box, computationally expensive to fit, highly susceptible to overfitting, or/and difficult to optimize for data selection. This paper proposes a framework called *<projektor>*, which predicts model performance and supports data selection decisions based on partial samples of prospective data sources. Our approach distinguishes itself from existing work by introducing a novel *two-stage* performance inference process. In the first stage, we leverage the Optimal Transport distance to predict the model's performance for any data mixture ratio within the range of disclosed data sizes. In the second stage, we extrapolate the performance to larger undisclosed data sizes based on a novel parameter-free mapping technique inspired by neural scaling laws. We further derive an efficient gradient-based method to select data sources based on the projected model performance. Evaluation over a diverse range of applications (e.g., vision, text, fine-tuning, noisy data sources, etc.) demonstrates that *<projektor>* significantly improves existing performance scaling approaches in terms of both the accuracy of performance inference and the computation costs associated with constructing the performance predictor. Also, *<projektor>* outperforms by a wide margin in data selection effectiveness compared to a range of other off-the-shelf solutions. We provide *<projektor>* an open-source toolkit.

Miscellaneous Aspects of Machine Learning/Representation Learning

JIAWEI DU, Qin Shi, Joey Tianyi Zhou

Dataset distillation is a newly emerging task that synthesizes a small-size dataset used in training deep neural networks (DNNs) for reducing data storage and model training costs. The synthetic datasets are expected to capture the essence of the knowledge contained in real-world datasets such that the former yields a similar performance as the latter. Recent advancements in distillation methods have produced notable improvements in generating synthetic datasets. However, current state-of-the-art methods treat the entire synthetic dataset as a unified entity and optimize each synthetic instance equally . This static optimization approach may lead to performance degradation in dataset distillation. Specifically, we argue that static optimization can give rise to a coupling issue within the synthetic data, particularly when a larger amount of synthetic data is being optimized. This coupling issue, in turn, leads to the failure of the distilled dataset to extract the high-level features learned by the deep neural network (DNN) in the latter epochs.In this study, we propose a new dataset distillation strategy called Sequential Subset Matching (SeqMatch), which tackles this problem by adaptively optimizing the synthetic data to encourage sequential acquisition of knowledge during dataset distillation. Our analysis indicates that SeqMatch effectively addresses the coupling issue by sequentially generating the synthetic instances, thereby enhancing its performance significantly. Our proposed SeqMatch outperforms state-of-the-art methods in various datasets, including SVNH, CIFAR-10, CIFAR-100, and Tiny ImageNet.

Miscellaneous Aspects of Machine Learning/Kernel methods

Matthew Fisher, Chris Oates

Stein discrepancies have emerged as a powerful statistical tool, being applied to fundamental statistical problems including parameter inference, goodness-of-fit testing, and sampling. The canonical Stein discrepancies require the derivatives of a statistical model to be computed, and in return provide theoretical guarantees of convergence detection and control. However, for complex statistical models, the stable numerical computation of derivatives can require bespoke algorithmic development and render Stein discrepancies impractical. This paper focuses on posterior approximation using Stein discrepancies, and introduces a collection of non-canonical Stein discrepancies that are gradient-free, meaning that derivatives of the statistical model are not required. Sufficient conditions for convergence detection and control are established, and applications to sampling and variational inference are presented.

Miscellaneous Aspects of Machine Learning/Unsupervised and Semi-supervised Learning

Zicheng Liu, Siyuan Li, Ge Wang, Lirong Wu, Cheng Tan, Stan Z. Li

Mixup is an efficient data augmentation approach that improves the generalization of neural networks by smoothing the decision boundary with mixed data. Recently, dynamic mixup methods have improved previous \textit{static} policies effectively (e.g., linear interpolation) by maximizing target-related salient regions in mixed samples, but excessive additional time costs are not acceptable. These additional computational overheads mainly come from optimizing the mixed samples according to the mixed labels. However, we found that the extra optimizing step may be redundant because label-mismatched mixed samples are informative hard mixed samples for deep models to localize discriminative features. In this paper, we thus are not trying to propose a more complicated dynamic mixup policy but rather an efficient mixup objective function with decoupled regularizer, named decoupled mixup (DM). The primary effect is that DM can adaptively utilize those hard mixed samples to mine discriminative features without losing the original smoothness of mixup. As a result, DM enables static mixup methods to achieve comparable or even exceed the performance of dynamic methods without any extra computation. This also leads to an interesting objective design problem for mixup training that we need to focus on both smoothing the decision boundaries and identifying discriminative features. Extensive experiments on supervised and semi-supervised learning benchmarks across seven datasets validate the effectiveness of DM.

Miscellaneous Aspects of Machine Learning/Causality

Qianyi Chen, Bo Li, Lu Deng, Yong Wang

Online A/B tests have become increasingly popular and important for social platforms. However, accurately estimating the global average treatment effect (GATE) has proven to be challenging due to network interference, which violates the Stable Unit Treatment Value Assumption (SUTVA) and poses great challenge to experimental design. Existing network experimental design research was mostly based on the unbiased Horvitz-Thompson (HT) estimator with substantial data trimming to ensure unbiasedness at the price of high resultant estimation variance. In this paper, we strive to balance the bias and variance in designing randomized network experiments. Under a potential outcome model with 1-hop interference, we derive the bias and variance of the standard HT estimator and reveal their relation to the network topological structure and the covariance of the treatment assignment vector. We then propose to formulate the experimental design problem as to optimize the covariance matrix of the treatment assignment vector to achieve the bias and variance balance by minimizing the mean squared error (MSE) of the estimator. An efficient projected gradient descent algorithm is presented to the implement of the desired randomization scheme. Finally, we carry out extensive simulation studies to demonstrate the advantages of our proposed method over other existing methods in many settings, with different levels of model misspecification.