Monotonic Learning in the PAC Framework: A New Perspective
- URL: http://arxiv.org/abs/2501.05493v1
- Date: Thu, 09 Jan 2025 12:26:11 GMT
- Title: Monotonic Learning in the PAC Framework: A New Perspective
- Authors: Ming Li, Chenyi Zhang, Qin Li,
- Abstract summary: Monotone learning refers to learning processes in which expected performance consistently improves as more training data is introduced.
We tackle the topic of monotone learning within the framework of Probably Approximately Correct (PAC) learning theory.
By calculating the lower bound distribution, we are able to prove that given a PAC-learnable problem with a hypothesis space that is either of finite size or of finite VC dimension, any learning algorithm based on Empirical Risk Minimization (ERM) is monotone.
- Score: 8.911102248548206
- License:
- Abstract: Monotone learning refers to learning processes in which expected performance consistently improves as more training data is introduced. Non-monotone behavior of machine learning has been the topic of a series of recent works, with various proposals that ensure monotonicity by applying transformations or wrappers on learning algorithms. In this work, from a different perspective, we tackle the topic of monotone learning within the framework of Probably Approximately Correct (PAC) learning theory. Following the mechanism that estimates sample complexity of a PAC-learnable problem, we derive a performance lower bound for that problem, and prove the monotonicity of that bound as the sample sizes increase. By calculating the lower bound distribution, we are able to prove that given a PAC-learnable problem with a hypothesis space that is either of finite size or of finite VC dimension, any learning algorithm based on Empirical Risk Minimization (ERM) is monotone if training samples are independent and identically distributed (i.i.d.). We further carry out an experiment on two concrete machine learning problems, one of which has a finite hypothesis set, and the other of finite VC dimension, and compared the experimental data for the empirical risk distributions with the estimated theoretical bound. The results of the comparison have confirmed the monotonicity of learning for the two PAC-learnable problems.
Related papers
- Model-free Methods for Event History Analysis and Efficient Adjustment (PhD Thesis) [55.2480439325792]
This thesis is a series of independent contributions to statistics unified by a model-free perspective.
The first chapter elaborates on how a model-free perspective can be used to formulate flexible methods that leverage prediction techniques from machine learning.
The second chapter studies the concept of local independence, which describes whether the evolution of one process is directly influenced by another.
arXiv Detail & Related papers (2025-02-11T19:24:09Z) - Unveiling the Statistical Foundations of Chain-of-Thought Prompting Methods [59.779795063072655]
Chain-of-Thought (CoT) prompting and its variants have gained popularity as effective methods for solving multi-step reasoning problems.
We analyze CoT prompting from a statistical estimation perspective, providing a comprehensive characterization of its sample complexity.
arXiv Detail & Related papers (2024-08-25T04:07:18Z) - 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) - Optimal Multi-Distribution Learning [88.3008613028333]
Multi-distribution learning seeks to learn a shared model that minimizes the worst-case risk across $k$ distinct data distributions.
We propose a novel algorithm that yields an varepsilon-optimal randomized hypothesis with a sample complexity on the order of (d+k)/varepsilon2.
arXiv Detail & Related papers (2023-12-08T16:06:29Z) - Sample-Efficient Learning of POMDPs with Multiple Observations In
Hindsight [105.6882315781987]
This paper studies the sample-efficiency of learning in Partially Observable Markov Decision Processes (POMDPs)
Motivated by real-world settings such as loading in game playing, we propose an enhanced feedback model called multiple observations in hindsight''
We show that sample-efficient learning is possible for two new subclasses of POMDPs: emphmulti-observation revealing POMDPs and emphdistinguishable POMDPs
arXiv Detail & Related papers (2023-07-06T09:39:01Z) - 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) - MaxMatch: Semi-Supervised Learning with Worst-Case Consistency [149.03760479533855]
We propose a worst-case consistency regularization technique for semi-supervised learning (SSL)
We present a generalization bound for SSL consisting of the empirical loss terms observed on labeled and unlabeled training data separately.
Motivated by this bound, we derive an SSL objective that minimizes the largest inconsistency between an original unlabeled sample and its multiple augmented variants.
arXiv Detail & Related papers (2022-09-26T12:04:49Z) - Pairwise Learning via Stagewise Training in Proximal Setting [0.0]
We combine adaptive sample size and importance sampling techniques for pairwise learning, with convergence guarantees for nonsmooth convex pairwise loss functions.
We demonstrate that sampling opposite instances at each reduces the variance of the gradient, hence accelerating convergence.
arXiv Detail & Related papers (2022-08-08T11:51:01Z) - Counterfactual Maximum Likelihood Estimation for Training Deep Networks [83.44219640437657]
Deep learning models are prone to learning spurious correlations that should not be learned as predictive clues.
We propose a causality-based training framework to reduce the spurious correlations caused by observable confounders.
We conduct experiments on two real-world tasks: Natural Language Inference (NLI) and Image Captioning.
arXiv Detail & Related papers (2021-06-07T17:47:16Z) - Robust Unsupervised Learning via L-Statistic Minimization [38.49191945141759]
We present a general approach to this problem focusing on unsupervised learning.
The key assumption is that the perturbing distribution is characterized by larger losses relative to a given class of admissible models.
We prove uniform convergence bounds with respect to the proposed criterion for several popular models in unsupervised learning.
arXiv Detail & Related papers (2020-12-14T10:36:06Z)
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.