Proper Learnability and the Role of Unlabeled Data

• URL: http://arxiv.org/abs/2502.10359v1
• Date: Fri, 14 Feb 2025 18:41:53 GMT
• Title: Proper Learnability and the Role of Unlabeled Data
• Authors: Julian Asilis, Siddartha Devic, Shaddin Dughmi, Vatsal Sharan, Shang-Hua Teng,
• Abstract summary: We show that there are problems whose proper learnability is logically undecidable, i.e., independent of the ZFC axioms. We then show all impossibility results which obstruct any characterization of proper learnability in the realizable PAC model.
• Score: 10.168670899305232
• License:
• Abstract: Proper learning refers to the setting in which learners must emit predictors in the underlying hypothesis class $H$, and often leads to learners with simple algorithmic forms (e.g. empirical risk minimization (ERM), structural risk minimization (SRM)). The limitation of proper learning, however, is that there exist problems which can only be learned improperly, e.g. in multiclass classification. Thus, we ask: Under what assumptions on the hypothesis class or the information provided to the learner is a problem properly learnable? We first demonstrate that when the unlabeled data distribution is given, there always exists an optimal proper learner governed by distributional regularization, a randomized generalization of regularization. We refer to this setting as the distribution-fixed PAC model, and continue to evaluate the learner on its worst-case performance over all distributions. Our result holds for all metric loss functions and any finite learning problem (with no dependence on its size). Further, we demonstrate that sample complexities in the distribution-fixed PAC model can shrink by only a logarithmic factor from the classic PAC model, strongly refuting the role of unlabeled data in PAC learning (from a worst-case perspective). We complement this with impossibility results which obstruct any characterization of proper learnability in the realizable PAC model. First, we observe that there are problems whose proper learnability is logically undecidable, i.e., independent of the ZFC axioms. We then show that proper learnability is not a monotone property of the underlying hypothesis class, and that it is not a local property (in a precise sense). Our impossibility results all hold even for the fundamental setting of multiclass classification, and go through a reduction of EMX learning (Ben-David et al., 2019) to proper classification which may be of independent interest.

Related papers

• Probably Approximately Precision and Recall Learning [62.912015491907994]
  Precision and Recall are foundational metrics in machine learning. One-sided feedback--where only positive examples are observed during training--is inherent in many practical problems. We introduce a PAC learning framework where each hypothesis is represented by a graph, with edges indicating positive interactions.
  arXiv  Detail & Related papers  (2024-11-20T04:21:07Z)
• On Characterizing and Mitigating Imbalances in Multi-Instance Partial Label Learning [57.18649648182171]
  We make contributions towards addressing a problem that hasn't been studied so far in the context of MI-PLL. We derive class-specific risk bounds for MI-PLL, while making minimal assumptions. Our theory reveals a unique phenomenon: that $sigma$ can greatly impact learning imbalances.
  arXiv  Detail & Related papers  (2024-07-13T20:56:34Z)
• Collaborative Learning with Different Labeling Functions [7.228285747845779]
  We study a variant of Collaborative PAC Learning, in which we aim to learn an accurate classifier for each of the $n$ data distributions. We show that, when the data distributions satisfy a weaker realizability assumption, sample-efficient learning is still feasible.
  arXiv  Detail & Related papers  (2024-02-16T04:32:22Z)
• Learnability, Sample Complexity, and Hypothesis Class Complexity for Regression Models [10.66048003460524]
  This work is inspired by the foundation of PAC and is motivated by the existing regression learning issues. The proposed approach, denoted by epsilon-Confidence Approximately Correct (epsilon CoAC), utilizes Kullback Leibler divergence (relative entropy) It enables the learner to compare hypothesis classes of different complexity orders and choose among them the optimum with the minimum epsilon.
  arXiv  Detail & Related papers  (2023-03-28T15:59:12Z)
• Differentially-Private Bayes Consistency [70.92545332158217]
  We construct a Bayes consistent learning rule that satisfies differential privacy (DP) We prove that any VC class can be privately learned in a semi-supervised setting with a near-optimal sample complexity.
  arXiv  Detail & Related papers  (2022-12-08T11:57:30Z)
• Learning versus Refutation in Noninteractive Local Differential Privacy [133.80204506727526]
  We study two basic statistical tasks in non-interactive local differential privacy (LDP): learning and refutation. Our main result is a complete characterization of the sample complexity of PAC learning for non-interactive LDP protocols.
  arXiv  Detail & Related papers  (2022-10-26T03:19:24Z)
• Semi-verified PAC Learning from the Crowd [7.594050968868919]
  We study the problem of crowdsourced PAC learning of threshold functions. We show that under the semi-verified model of Charikar et al., it is possible to PAC learn the underlying hypothesis class with a manageable amount of label queries.
  arXiv  Detail & Related papers  (2021-06-13T20:05:16Z)
• Risk Minimization from Adaptively Collected Data: Guarantees for Supervised and Policy Learning [57.88785630755165]
  Empirical risk minimization (ERM) is the workhorse of machine learning, but its model-agnostic guarantees can fail when we use adaptively collected data. We study a generic importance sampling weighted ERM algorithm for using adaptively collected data to minimize the average of a loss function over a hypothesis class. For policy learning, we provide rate-optimal regret guarantees that close an open gap in the existing literature whenever exploration decays to zero.
  arXiv  Detail & Related papers  (2021-06-03T09:50:13Z)
• A Theory of Universal Learning [26.51949485387526]
  We show that there are only three possible rates of universal learning. We show that the learning curves of any given concept class decay either at an exponential, or arbitrarily slow rates.
  arXiv  Detail & Related papers  (2020-11-09T15:10:32Z)
• Probably Approximately Correct Constrained Learning [135.48447120228658]
  We develop a generalization theory based on the probably approximately correct (PAC) learning framework. We show that imposing a learner does not make a learning problem harder in the sense that any PAC learnable class is also a constrained learner. We analyze the properties of this solution and use it to illustrate how constrained learning can address problems in fair and robust classification.
  arXiv  Detail & Related papers  (2020-06-09T19:59:29Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.