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Probabilistic Methods · Bayesian Models and Methods

Parikshit Pareek, Abhijith Jayakumar, Kaarthik Sundar, Sidhant Misra, Deepjyoti Deka

Constrained optimization problems arise in various engineering systems such as inventory management and power grids. Standard deep neural network (DNN) based machine learning proxies are ineffective in practical settings where labeled data is scarce and training times are limited. We propose a semi-supervised Bayesian Neural Networks (BNNs) based optimization proxy for this complex regime, wherein training commences in a sandwiched fashion, alternating between a supervised learning step for minimizing cost, and an unsupervised learning step for enforcing constraint feasibility. We show that the proposed semi-supervised BNN outperforms DNN architectures on important non-convex constrained optimization problems from energy network operations, achieving up to a tenfold reduction in expected maximum equality gap and halving the inequality gaps. Further, the BNN's ability to provide posterior samples is leveraged to construct practically meaningful probabilistic confidence bounds on performance using a limited validation data, unlike prior methods.

General Machine Learning · Unsupervised and Semi-supervised Learning

Yifan Fang, Yifei Fang, Ruizhe Chen, Haote Xu, Xinghao Ding, Yue Huang

Frequency-domain image anomaly detection methods can substantially enhance anomaly detection performance, however, they still lack an interpretable theoretical framework to guarantee the effectiveness of the detection process. We propose a novel test to detect anomalies in structural image via a Demeaned Fourier transform (DFT) under factor model framework, and we proof its effectiveness. We also briefly give the asymptotic theories of our test, the asymptotic theory explains why the test can detect anomalies at both the image and pixel levels within the theoretical lower bound. Based on our test, we derive a module called Demeaned Fourier Sparse (DFS) that effectively enhances detection performance in unsupervised anomaly detection tasks, which can construct masks in the Fourier domain and utilize a distribution-free sampling method similar to the bootstrap method. The experimental results indicate that this module can accurately and efficiently generate effective masks for reconstruction-based anomaly detection tasks, thereby enhancing the performance of anomaly detection methods and validating the effectiveness of the theoretical framework.

General Machine Learning · Unsupervised and Semi-supervised Learning

Mohammad Jalali, Bahar Dibaei Nia, Farzan Farnia

While several feature embedding models have been developed in the literature, comparisons of these embeddings have largely focused on their numerical performance in classification-related downstream applications. However, an interpretable comparison of different embeddings requires identifying and analyzing mismatches between sample groups clustered within the embedding spaces. In this work, we propose the Spectral Pairwise Embedding Comparison (SPEC) framework to compare embeddings and identify their differences in clustering a reference dataset. Our approach examines the kernel matrices derived from two embeddings and leverages the eigendecomposition of the difference kernel matrix to detect sample clusters that are captured differently by the two embeddings. We present a scalable implementation of this kernel-based approach, with computational complexity that grows linearly with the sample size. Furthermore, we introduce an optimization problem using this framework to align two embeddings, ensuring that clusters identified in one embedding are also captured in the other model. We provide numerical results demonstrating the SPEC's application to compare and align embeddings on large-scale datasets such as ImageNet and MS-COCO. The code is available at [https://github.com/mjalali/embedding-comparison](github.com/mjalali/embedding-comparison).

General Machine Learning · Unsupervised and Semi-supervised Learning

Erez Peterfreund, Ofir Lindenbaum, Yuval Kluger, Boris Landa

Embedding and visualization techniques are essential for analyzing high-dimensional data, but they often struggle with complex data governed by multiple latent variables, potentially distorting key structural characteristics. This paper considers scenarios where the observed features can be partitioned into mutually exclusive subsets, each capturing a different smooth substructure. In such cases, visualizing the data based on each feature partition can better characterize the underlying processes and structures in the data, leading to improved interpretability. To partition the features, we propose solving an optimization problem that promotes graph Laplacian-based smoothness in each partition, thereby prioritizing partitions with simpler geometric structures. Our approach generalizes traditional embedding and visualization techniques, allowing them to learn multiple embeddings simultaneously. We establish that if several independent or partially dependent manifolds are embedded in distinct feature subsets in high-dimensional space, then our framework can reliably identify the correct subsets with theoretical guarantees. Finally, we demonstrate the effectiveness of our approach in extracting multiple low-dimensional structures and partially independent processes from both simulated and real data.

General Machine Learning · Unsupervised and Semi-supervised Learning

Erez Peterfreund, Ofir Lindenbaum, Yuval Kluger, Boris Landa

Embedding and visualization techniques are essential for analyzing high-dimensional data, but they often struggle with complex data governed by multiple latent variables, potentially distorting key structural characteristics. This paper considers scenarios where the observed features can be partitioned into mutually exclusive subsets, each capturing a different smooth substructure. In such cases, visualizing the data based on each feature partition can better characterize the underlying processes and structures in the data, leading to improved interpretability. To partition the features, we propose solving an optimization problem that promotes graph Laplacian-based smoothness in each partition, thereby prioritizing partitions with simpler geometric structures. Our approach generalizes traditional embedding and visualization techniques, allowing them to learn multiple embeddings simultaneously. We establish that if several independent or partially dependent manifolds are embedded in distinct feature subsets in high-dimensional space, then our framework can reliably identify the correct subsets with theoretical guarantees. Finally, we demonstrate the effectiveness of our approach in extracting multiple low-dimensional structures and partially independent processes from both simulated and real data.

General Machine Learning · Unsupervised and Semi-supervised Learning

Alex Kokot, Octavian-Vlad Murad, Marina Meila

In this paper, we clarify the effect of noise on common spectrallymotivated algorithms such as Diffusion Maps (DM) for dimensionreduction. Empirically, these methods are much more robust to noisethan current work suggests. Specifically, existing consistency resultsrequire that either the noise amplitude or dimensionality must varywith the sample size $n$. We provide new theoretical resultsdemonstrating that low-frequency eigenpairs reliably capture thegeometry of the underlying manifold under a constant noise level, up to a dimension independent threshold $O(r^{-2})$, where $r$ is the noise amplitude. Our results rely on a decomposition of the manifold Laplacian in the Sasakimetric, a technique not used before in this area, to our knowledge. We experimentally validate our theoretical predictions. Additionally, we observesimilar robust behavior for other manifold learning algorithms which are not based on computing the Laplacian, namely LTSA and VAE.

General Machine Learning · Unsupervised and Semi-supervised Learning

Bowen Deng, Lele Fu, Jialong Chen, Sheng Huang, Tianchi Liao, Zhang Tao, Chuan Chen

Generalized Category Discovery (GCD) aims to identify both known and novel categories in unlabeled data by leveraging knowledge from old classes. However, existing methods are limited to non-graph data; lack theoretical foundations to answer *When and how known classes can help GCD*. We introduce the Graph GCD task; provide the first rigorous theoretical analysis of *parametric GCD*. By quantifying the relationship between old and new classes in the embedding space using the Wasserstein distance W, we derive the first provable GCD loss bound based on W. This analysis highlights two necessary conditions for effective GCD. However, we uncover, through a Pairwise Markov Random Field perspective, that popular graph contrastive learning (GCL) methods inherently violate these conditions. To address this limitation, we propose SWIRL, a novel GCL method for GCD. Experimental results validate our (theoretical) findings and demonstrate SWIRL's effectiveness.

General Machine Learning · Unsupervised and Semi-supervised Learning

Leonardo Hernandez Cano, Maxine Perroni-Scharf, Neil Dhir, Arun Ramamurthy, Armando Solar-Lezama

We present Structured World Modeling for Policy Optimization (SWMPO), a framework for unsupervised learning of neurosymbolic Finite State Machines (FSM) that capture environmental structure for policy optimization. Traditional unsupervised world modeling methods rely on unstructured representations, such as neural networks, that do not explicitly represent high-level patterns within the system (e.g., patterns in the dynamics of regions such as \emph{water} and \emph{land}).Instead, SWMPO models the environment as a finite state machine (FSM), where each state corresponds to a specific region with distinct dynamics. This structured representation can then be leveraged for tasks like policy optimization. Previous works that synthesize FSMs for this purpose have been limited to discrete spaces, not continuous spaces. Instead, our proposed FSM synthesis algorithm operates in an unsupervised manner, leveraging low-level features from unprocessed, non-visual data, making it adaptable across various domains. The synthesized FSM models are expressive enough to be used in a model-based Reinforcement Learning scheme that leverages offline data to efficiently synthesize environment-specific world models.We demonstrate the advantages of SWMPO by benchmarking its environment modeling capabilities in simulated environments.

General Machine Learning · Unsupervised and Semi-supervised Learning

Meilin Wang, Wei Huang, Mingming Gong, Zheng Zhang

*Density ratio estimation* (DRE) is a paramount task in machine learning, for its broad applications across multiple domains, such as covariate shift adaptation, causal inference, independence tests and beyond. Parametric methods for estimating the density ratio possibly lead to biased results if models are misspecified, while conventional non-parametric methods suffer from the curse of dimensionality when the dimension of data is large. To address these challenges, in this paper, we propose a novel approach for DRE based on the projection pursuit (PP) approximation. The proposed method leverages PP to mitigate the impact of high dimensionality while retaining the model flexibility needed for the accuracy of DRE. We establish the consistency and the convergence rate for the proposed estimator. Experimental results demonstrate that our proposed method outperforms existing alternatives in various applications.

General Machine Learning · Unsupervised and Semi-supervised Learning

Josh Givens, Song Liu, Henry Reeve

Score matching is a vital tool for learning the distribution of data with applications across many areas including diffusion processes, energy based modelling, and graphical model estimation. Despite all these applications, little work explores its use when data is incomplete. We address this by adapting score matching (and its major extensions) to work with missing data in a flexible setting where data can be partially missing over any subset of the coordinates. We provide two separate score matching variations for general use, an importance weighting (IW) approach, and a variational approach. We provide finite sample bounds for our IW approach in finite domain settings and show it to have especially strong performance in small sample lower dimensional cases. Complementing this, we show our variational approach to be strongest in more complex high-dimensional settings which we demonstrate on graphical model estimation tasks on both real and simulated data.

General Machine Learning · Unsupervised and Semi-supervised Learning

Yuchen Wang, Xuefeng Bai, Xiucheng Li, Weili Guan, Liqiang Nie, Xinyang Chen

Adapting vision-language models (VLMs) to downstream tasks with pseudolabels has gained increasing attention. A major obstacle is that the pseudolabels generated by VLMs tend to be imbalanced, leading to inferior performance.While existing methods have explored various strategies to address this, the underlying causes of imbalance remain insufficiently investigated.To fill this gap, we delve into imbalanced pseudolabels and identify two primary contributing factors: concept mismatch and concept confusion. To mitigate these two issues, we propose a novel framework incorporating concept alignment and confusion-aware calibrated margin mechanisms. The core of our approach lies in enhancing underperforming classes and promoting balanced predictions across categories, thus mitigating imbalance. Extensive experiments on six benchmark datasets with three learning paradigms demonstrate that the proposed method effectively enhances the accuracy and balance of pseudolabels, achieving a relative improvement of 6.29\% over the SoTA method. Our code is avaliable at https://github.com/Noahwangyuchen/CAP

General Machine Learning · Unsupervised and Semi-supervised Learning

Lin-Han Jia, Wen-Chao Hu, Jie-Jing Shao, Lan-Zhe Guo, Yu-Feng Li

The current Neuro-Symbolic (NeSy) Learning paradigm suffers from an over-reliance on labeled data, so if we completely disregard labels, it leads to less symbol information, a larger solution space, and more shortcuts—issues that current Nesy systems cannot resolve. This paper introduces a novel learning paradigm, Verification Learning (VL), which addresses this challenge by transforming the label-based reasoning process in Nesy into a label-free verification process. VL achieves excellent learning results solely by relying on unlabeled data and a function that verifies whether the current predictions conform to the rules. We formalize this problem as a Constraint Optimization Problem (COP) and propose a Dynamic Combinatorial Sorting (DCS) algorithm that accelerates the solution by reducing verification attempts, effectively lowering computational costs and introduce a prior alignment method to address potential shortcuts. Our theoretical analysis points out which tasks in Nesy systems can be completed without labels and explains why rules can replace infinite labels for some tasks, while for others the rules have no effect. We validate the proposed framework through several fully unsupervised tasks including addition, sort, match, and chess, each showing significant performance and efficiency improvements.

General Machine Learning · Unsupervised and Semi-supervised Learning

Pan Du, Zhao, Xinai Lu, Nian Liu, Zhikai Li, Chaoyu Gong, Suyun Zhao, Hong Chen, Cuiping Li, Kai Wang 等

Class distribution mismatch (CDM) refers to the discrepancy between class distributions in training data and target tasks. Previous methods address this by designing classifiers to categorize classes known during training, while grouping unknown or new classes into an "other" category. However, they focus on semi-supervised scenarios and heavily rely on labeled data, limiting their applicability and performance. To address this, we propose Unsupervised Learning for Class Distribution Mismatch (UCDM), which constructs positive-negative pairs from unlabeled data for classifier training. Our approach randomly samples images and uses a diffusion model to add or erase semantic classes, synthesizing diverse training pairs. Additionally, we introduce a confidence-based labeling mechanism that iteratively assigns pseudo-labels to valuable real-world data and incorporates them into the training process. Extensive experiments on three datasets demonstrate UCDM’s superiority over previous semi-supervised methods. Specifically, with a 60\% mismatch proportion on Tiny-ImageNet dataset, our approach, without relying on labeled data, surpasses OpenMatch (with 40 labels per class) by 35.1%, 63.7%, and 72.5% in classifying known, unknown, and new classes.

General Machine Learning · Unsupervised and Semi-supervised Learning

Yaxin Hou, Yuheng Jia

This paper studies the long-tailed semi-supervised learning (LTSSL) with distribution mismatch, where the class distribution of the labeled training data follows a long-tailed distribution and mismatches with that of the unlabeled training data. Most existing methods introduce auxiliary classifiers (experts) to model various unlabeled data distributions and produce pseudo-labels, but the expertises of various experts are not fully utilized. We observe that different experts are good at predicting different intervals of samples, e.g., long-tailed expert is skilled in samples located in the head interval and uniform expert excels in samples located in the medium interval. Therefore, we propose a dynamic expert assignment module that can estimate the class membership (i.e., head, medium, or tail class) of samples, and dynamically assigns suitable expert to each sample based on the estimated membership to produce high-quality pseudo-label in the training phase and produce prediction in the testing phase. We also theoretically reveal that integrating different experts' strengths will lead to a smaller generalization error bound. Moreover, we find that the deeper features are more biased toward the head class but with more discriminative ability, while the shallower features are less biased but also with less discriminative ability. We, therefore, propose a multi-depth feature fusion module to utilize different depth features to mitigate the model bias. Our method demonstrates its effectiveness through comprehensive experiments on the CIFAR-10-LT, STL-10-LT, and SVHN-LT datasets across various settings. The code is available at https://github.com/yaxinhou/Meta-Expert.

General Machine Learning · Unsupervised and Semi-supervised Learning

Walid Durani, Tobias Nitzl, Claudia Plant, Christian Böhm

Detecting anomalies with limited supervision is challenging due to the scarcity of labeled anomalies, which often fail to capture the diversity of abnormal behaviors. We propose Weakly Supervised Anomaly Detection via Dual-Tailed Kernel (WSAD-DT), a novel framework that learns robust latent representations to distinctly separate anomalies from normal samples under weak supervision. WSAD-DT introduces two centroids—one for normal samples and one for anomalies—and leverages a dual-tailed kernel scheme: a light-tailed kernel to compactly model in-class points and a heavy-tailed kernel to main- tain a wider margin against out-of-class instances. To preserve intra-class diversity, WSAD-DT in- corporates kernel-based regularization, encouraging richer representations within each class. Furthermore, we devise an ensemble strategy that partition unlabeled data into diverse subsets, while sharing the limited labeled anomalies among these partitions to maximize their impact. Empirically, WSAD-DT achieves state-of-the-art performance on several challenging anomaly detection benchmarks, outperforming leading ensemble-based methods such as XGBOD.

General Machine Learning · Unsupervised and Semi-supervised Learning

Duo Liu, Zhiquan Tan, Linglan Zhao, Zhongqiang Zhang, Xiangzhong Fang, Weiran Huang

Generalized Category Discovery (GCD) aims to identify unlabeled samples by leveraging the base knowledge from labeled ones, where the unlabeled set consists of both base and novel classes. Since clustering methods are time-consuming at inference, parametric-based approaches have become more popular. However, recent parametric-based methods suffer from inferior base discrimination due to unreliable self-supervision. To address this issue, we propose a Reciprocal Learning Framework (RLF) that introduces an auxiliary branch devoted to base classification. During training, the main branch filters the pseudo-base samples to the auxiliary branch. In response, the auxiliary branch provides more reliable soft labels for the main branch, leading to a virtuous cycle. Furthermore, we introduce Class-wise Distribution Regularization (CDR) to mitigate the learning bias towards base classes. CDR essentially increases the prediction confidence of the unlabeled data and boosts the novel class performance. Combined with both components, our proposed method, RLCD, achieves superior performance in all classes with negligible extra computation. Comprehensive experiments across seven GCD datasets validate its superiority.Our codes are available at https://github.com/APORduo/RLCD.

General Machine Learning · Unsupervised and Semi-supervised Learning

chao ying, Jun Jin, Yi Guo, Xiudi Li, Muxuan Liang, Jiwei Zhao

Collecting gold-standard phenotype data via manual extraction is typically labor-intensive and slow, whereas automated computational phenotypes (ACPs) offer a systematic and much faster alternative.However, simply replacing the gold-standard with ACPs, without acknowledging their differences, could lead to biased results and misleading conclusions.Motivated by the complexity of incorporating ACPs while maintaining the validity of downstream analyses, in this paper, we consider a semi-supervised learning setting that consists of both labeled data (with gold-standard) and unlabeled data (without gold-standard), under the covariate shift framework.We develop doubly robust and semiparametrically efficient estimators that leverage ACPs for general target parameters in the unlabeled and combined populations. In addition,we carefully analyze the efficiency gains achieved by incorporating ACPs, comparing scenarios with and without their inclusion.Notably, we identify that ACPs for the unlabeled data, instead of for the labeled data, drive the enhanced efficiency gains. To validate our theoretical findings, we conduct comprehensive synthetic experiments and apply our method to multiple real-world datasets, confirming the practical advantages of our approach.

General Machine Learning · Unsupervised and Semi-supervised Learning

Aditya Gorla, Ryan Wang, Zhengtong Liu, Ulzee An, Sriram Sankararaman

We present CACTI, a masked autoencoding approach for imputing tabular data that leverages the structure in missingness patterns and contextual information. Our approach employs a novel median truncated copy masking training strategy that encourages the model to learn from empirical patterns of missingness while incorporating semantic relationships between features — captured by column names and text descriptions — to better represent feature dependence. These dual sources of inductive bias enable CACTIto outperform state-of-the-art methods — an average $R^2$ gain of 7.8\% over the next best method (13.4%, 6.1%, and 5.3% under missing not at random, at random and completely at random, respectively) — across a diverse range of datasets and missingness conditions. Our results highlight the value of leveraging dataset-specific contextual information and missingness patterns to enhance imputation performance.

General Machine Learning · Unsupervised and Semi-supervised Learning

Abhijeet Mulgund, Chirag Pabbaraju

The paradigm of weak-to-strong generalization constitutes the training of a strong AI model on data labeled by a weak AI model, with the goal that the strong model nevertheless outperforms its weak supervisor on the target task of interest. For the setting of real-valued regression with the squared loss, recent work quantitatively characterizes the gain in performance of the strong model over the weak model in terms of the misfit between the strong and weak model. We generalize such a characterization to learning tasks whose loss functions correspond to arbitrary Bregman divergences when the strong class is convex. This extends the misfit-based characterization of performance gain in weak-to-strong generalization to classification tasks, as the cross-entropy loss can be expressed in terms of a Bregman divergence. In most practical scenarios, however, the strong model class may not be convex. We therefore weaken this assumption and study weak-to-strong generalization for convex combinations of $k$ strong models in the strong class, in the concrete setting of classification. This allows us to obtain a similar misfit-based characterization of performance gain, up to an additional error term that vanishes as $k$ gets large. Our theoretical findings are supported by thorough experiments on synthetic as well as real-world datasets.

General Machine Learning · Unsupervised and Semi-supervised Learning

Vincent P. Grande, Michael Schaub

Topological Data Analysis (TDA) allows us to extract powerful topological and higher-order information on the global shape of a data set or point cloud.Tools like Persistent Homology give a single complex description of the global structure of the point cloud.However, common machine learning applications like classification require point-level information and features.In this paper, we bridge this gap and propose a novel method to extract node-level topological features from complex point clouds using discrete variants of concepts from algebraic topology and differential geometry.We verify the effectiveness of these topological point features (TOPF) on both synthetic and real-world data and study their robustness under noise and heterogeneous sampling.