Gauge-optimal approximate learning for small data classification problems

• URL: http://arxiv.org/abs/2310.19066v1
• Date: Sun, 29 Oct 2023 16:46:05 GMT
• Title: Gauge-optimal approximate learning for small data classification problems
• Authors: Edoardo Vecchi, Davide Bassetti, Fabio Graziato, Lukas Pospisil, Illia Horenko
• Abstract summary: Small data learning problems are characterized by a discrepancy between the limited amount of response variable observations and the large feature space dimension. We propose the Gauge- Optimal Approximate Learning (GOAL) algorithm, which provides an analytically tractable joint solution to the reduction dimension, feature segmentation and classification problems. GOAL has been compared to other state-of-the-art machine learning (ML) tools on both synthetic data and challenging real-world applications from climate science and bioinformatics.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Small data learning problems are characterized by a significant discrepancy between the limited amount of response variable observations and the large feature space dimension. In this setting, the common learning tools struggle to identify the features important for the classification task from those that bear no relevant information, and cannot derive an appropriate learning rule which allows to discriminate between different classes. As a potential solution to this problem, here we exploit the idea of reducing and rotating the feature space in a lower-dimensional gauge and propose the Gauge-Optimal Approximate Learning (GOAL) algorithm, which provides an analytically tractable joint solution to the dimension reduction, feature segmentation and classification problems for small data learning problems. We prove that the optimal solution of the GOAL algorithm consists in piecewise-linear functions in the Euclidean space, and that it can be approximated through a monotonically convergent algorithm which presents -- under the assumption of a discrete segmentation of the feature space -- a closed-form solution for each optimization substep and an overall linear iteration cost scaling. The GOAL algorithm has been compared to other state-of-the-art machine learning (ML) tools on both synthetic data and challenging real-world applications from climate science and bioinformatics (i.e., prediction of the El Nino Southern Oscillation and inference of epigenetically-induced gene-activity networks from limited experimental data). The experimental results show that the proposed algorithm outperforms the reported best competitors for these problems both in learning performance and computational cost.

Related papers

• On Probabilistic Embeddings in Optimal Dimension Reduction [1.2085509610251701]
  Dimension reduction algorithms are a crucial part of many data science pipelines. Despite their wide utilization, many non-linear dimension reduction algorithms are poorly understood from a theoretical perspective.
  arXiv  Detail & Related papers  (2024-08-05T12:46:21Z)
• Nonconvex Federated Learning on Compact Smooth Submanifolds With Heterogeneous Data [23.661713049508375]
  We propose an algorithm that learns over a submanifold in the setting of a client. We show that our proposed algorithm converges sub-ly to a neighborhood of a first-order optimal solution by using a novel analysis.
  arXiv  Detail & Related papers  (2024-06-12T17:53:28Z)
• Towards model-free RL algorithms that scale well with unstructured data [1.3799571823220778]
  We provide an algorithm that constructs reward-relevant general value function questions to find and exploit predictive structure directly from the experience stream. The proposed algorithm reliably outperforms a conventional deep RL algorithm on these scaling problems.
  arXiv  Detail & Related papers  (2023-11-03T20:03:54Z)
• Efficient Model-Free Exploration in Low-Rank MDPs [76.87340323826945]
  Low-Rank Markov Decision Processes offer a simple, yet expressive framework for RL with function approximation. Existing algorithms are either (1) computationally intractable, or (2) reliant upon restrictive statistical assumptions. We propose the first provably sample-efficient algorithm for exploration in Low-Rank MDPs.
  arXiv  Detail & Related papers  (2023-07-08T15:41:48Z)
• Nonlinear Feature Aggregation: Two Algorithms driven by Theory [45.3190496371625]
  Real-world machine learning applications are characterized by a huge number of features, leading to computational and memory issues. We propose a dimensionality reduction algorithm (NonLinCFA) which aggregates non-linear transformations of features with a generic aggregation function. We also test the algorithms on synthetic and real-world datasets, performing regression and classification tasks, showing competitive performances.
  arXiv  Detail & Related papers  (2023-06-19T19:57:33Z)
• Representation Learning with Multi-Step Inverse Kinematics: An Efficient and Optimal Approach to Rich-Observation RL [106.82295532402335]
  Existing reinforcement learning algorithms suffer from computational intractability, strong statistical assumptions, and suboptimal sample complexity. We provide the first computationally efficient algorithm that attains rate-optimal sample complexity with respect to the desired accuracy level. Our algorithm, MusIK, combines systematic exploration with representation learning based on multi-step inverse kinematics.
  arXiv  Detail & Related papers  (2023-04-12T14:51:47Z)
• Learning to Bound Counterfactual Inference in Structural Causal Models from Observational and Randomised Data [64.96984404868411]
  We derive a likelihood characterisation for the overall data that leads us to extend a previous EM-based algorithm. The new algorithm learns to approximate the (unidentifiability) region of model parameters from such mixed data sources. It delivers interval approximations to counterfactual results, which collapse to points in the identifiable case.
  arXiv  Detail & Related papers  (2022-12-06T12:42:11Z)
• A Differentiable Approach to Combinatorial Optimization using Dataless Neural Networks [20.170140039052455]
  We propose a radically different approach in that no data is required for training the neural networks that produce the solution. In particular, we reduce the optimization problem to a neural network and employ a dataless training scheme to refine the parameters of the network such that those parameters yield the structure of interest.
  arXiv  Detail & Related papers  (2022-03-15T19:21:31Z)
• Simple Stochastic and Online Gradient DescentAlgorithms for Pairwise Learning [65.54757265434465]
  Pairwise learning refers to learning tasks where the loss function depends on a pair instances. Online descent (OGD) is a popular approach to handle streaming data in pairwise learning. In this paper, we propose simple and online descent to methods for pairwise learning.
  arXiv  Detail & Related papers  (2021-11-23T18:10:48Z)
• Generalization of Neural Combinatorial Solvers Through the Lens of Adversarial Robustness [68.97830259849086]
  Most datasets only capture a simpler subproblem and likely suffer from spurious features. We study adversarial robustness - a local generalization property - to reveal hard, model-specific instances and spurious features. Unlike in other applications, where perturbation models are designed around subjective notions of imperceptibility, our perturbation models are efficient and sound. Surprisingly, with such perturbations, a sufficiently expressive neural solver does not suffer from the limitations of the accuracy-robustness trade-off common in supervised learning.
  arXiv  Detail & Related papers  (2021-10-21T07:28:11Z)
• Learning Neural Causal Models with Active Interventions [83.44636110899742]
  We introduce an active intervention-targeting mechanism which enables a quick identification of the underlying causal structure of the data-generating process. Our method significantly reduces the required number of interactions compared with random intervention targeting. We demonstrate superior performance on multiple benchmarks from simulated to real-world data.
  arXiv  Detail & Related papers  (2021-09-06T13:10:37Z)

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.