New theory challenges traditional machine learning assumptions.
problem Traditional machine learning theories are critiqued.
method A new theory is proposed and discussed.
result Learning true probabilities is not equivalent to other learning goals.
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48 results for “Machine learning theory”
Machine learning explores symmetries in field theory and algebra.
problem Understanding symmetries in field theory and algebra.
method Using neural networks to analyze conformal field theory and Lie algebra representation theory.
result Recent advances in machine learning have uncovered new symmetries.
(K)not machine learninghep-th
Machine learning knot invariants with physics applications.
problem Understanding relations between knot invariants in physics.
method Machine learning and theoretical physics (Chern-Simons theory, gauge theories).
result New analytic results from Big Data experiments.
Abstract: Surveying connections between ML and Control Theory.
problem Addressing the intersection of Machine Learning and Control Theory.
method Develops connections through reinforcement learning, supervised learning, deep learning, and stochastic gradient descent.
result Machine Learning and Control Theory are interconnected, with ML solving large control problems and Control Theory providing tools for ML.
Review and Prospect of Algebraic Research in Equivalent Framework between Statistical Mechanics and Machine Learning Theorycond-mat.stat-mech
Paper reviews algebraic research in machine learning theory.
problem Understanding phase transitions in machine learning models.
method Algebraic approaches in statistical mechanics.
result Algebraic methods are essential for analyzing machine learning models with singularities.
Machine learning uses invariant theory to restrict function classes.
problem Creating function classes that respect physical law constraints.
method Using equivariant machine learning and Malgrance's method to parameterize functions.
result Explicitly parameterizes equivariant functions between linear spaces.
New theory uses probability sets for data variability, improving machine learning.
problem Variability in data distribution causes learning issues.
method Uses convex sets of probabilities (credal sets) to model data variability.
result Derives bounds for risk of models learned from multiple training sets.
Two different views on machine learning problem: Applied learning (machine learning with business applications) and Agnostic PAC learning are formalized and compared here. I show that, under some conditions, the theory of PAC Learnable provides a way to solve the Applied learning problem. However, the theory requires t…
This paper introduces a novel measure-theoretic theory for machine learning that does not require statistical assumptions. Based on this theory, a new regularization method in deep learning is derived and shown to outperform previous methods in CIFAR-10, CIFAR-100, and SVHN. Moreover, the proposed theory provides a the…
GQML uses symmetries from representation theory to improve quantum machine learning.
problem Creating quantum models with symmetries to improve performance.
method Introduction to representation theory for quantum learning, focusing on group actions and symmetries.
result Effective implementation of GQML requires knowledge of group representation theory.
DisCoPyro combines category theory with machine learning for program learning.
problem Applying category theory to machine learning tasks.
method Introducing DisCoPyro, a framework combining categorical structures with amortized variational inference.
result DisCoPyro can be applied in program learning for variational autoencoders and potentially contributes to AGI.
Statistical learning theory provides the theoretical basis for many of today's machine learning algorithms. In this article we attempt to give a gentle, non-technical overview over the key ideas and insights of statistical learning theory. We target at a broad audience, not necessarily machine learning researchers. Thi…
GeoShapley uses game theory to measure spatial effects in ML models.
problem Measuring the impact of location on machine learning model predictions.
method Extends Shapley value framework to quantify spatial effects in various ML models.
result Validated GeoShapley values against known processes and demonstrated utility in house price modeling.
The main goal of statistical learning theory is to provide a fundamental framework for the problem of decision making and model construction based on sets of data. Here, we present a brief introduction to the fundamentals of statistical learning theory, in particular the difference between empirical and structural risk…
Graph machine learning lacks a balanced theory, focusing on expressive power and optimization.
problem Insufficient theoretical understanding of GNNs' generalization behavior.
method Develop a balanced theory focusing on expressive power, generalization, and optimization.
result Theoretical advancements need to align with practical success in graph machine learning.
The paper connects machine learning interpretability with learning theory.
problem Performance and explanation generalization in local machine learning models.
method Theoretical analysis and empirical validation of local approximation explanations.
result Theoretical bounds on test-time accuracy and explanation generalization.
Information Theory in Open-world Machine Learning Foundations, Frameworks, and Future Directionstat.ML
This paper reviews information theory in open-world machine learning.
problem Lack of a unified theoretical foundation for open-world machine learning.
method Synthesis of information theoretic approaches.
result Established a pathway toward provable and trustworthy open world intelligence.
The paper develops a theory explaining how machine learning models can amplify biases.
problem Understanding and mitigating bias in machine learning models.
method Analytical theory of ridge regression with and without random projections.
result Observations and predictions align with empirical data on machine learning bias.
Study of machine learning in quiver gauge theories and Seiberg duality.
problem Determining dualities in quiver gauge theories using machine learning.
method Defined and explored various questions related to binary and multi-class duality determination, evaluated performance of different classifiers, and analyzed effects of additional data.
result High accuracy and confidence achieved in determining dualities using machine learning.
Machine Learning has become very famous currently which assist in identifying the patterns from the raw data. Technological advancement has led to substantial improvement in Machine Learning which, thus helping to improve prediction. Current Machine Learning models are based on Classical Theory, which can be replaced b…
Machine learning should incorporate maximum likelihood for better estimation.
problem Lack of rigorous foundational theory in machine learning.
method Integrate maximum likelihood estimation into machine learning models.
result Foundationally rigorous machine learning models have greater practical impact.
ART improves transfer learning performance with robust theory and methods.
problem Improving performance of primary tasks using auxiliary data.
method Adaptive Robust Transfer Learning (ART) pipeline with theoretical guarantees.
result ART provides a provable theoretical guarantee for adaptive transfer and robustness.
This work uses statistical mechanics to explain AI learning.
problem Understanding the statistical principles behind AI learning.
method Starting from sample concentration behaviors, the study applies statistical mechanics principles to AI and machine learning.
result Exponential families and statistical quantities are key in AI and machine learning.
Though the deep learning is pushing the machine learning to a new stage, basic theories of machine learning are still limited. The principle of learning, the role of the a prior knowledge, the role of neuron bias, and the basis for choosing neural transfer function and cost function, etc., are still far from clear. In …
Examines challenges and proposes new approaches in machine learning theory.
problem Challenges in machine learning as a function approximation and optimization.
method Mathematical analysis of gradient descent, fixed network limitations, and RNNs.
result New insights and mathematical approaches to improve machine learning.
The paper proposes a new portfolio allocation method combining RMT and machine learning.
problem Optimal allocation instability in high-dimensional portfolios.
method Combines Random Matrix Theory covariance estimators with Nested Clustered Optimization.
result The modified NCO algorithm achieves stable allocations without risky short positions.
Federated learning linked to mean-field games for large-scale learning.
problem Large-scale distributed and privacy-preserving learning algorithms.
method Established a connection between federated learning and mean-field games, presenting federated learning as a differential game.
result Properties of the equilibrium of the federated learning game were discussed.
Theory and methods to mitigate omitted variable bias in causal machine learning.
problem Mitigating omitted variable bias in causal machine learning models.
method Developed a general theory and flexible statistical inference methods for bounding and testing the magnitude of omitted variable bias.
result Simple plausibility judgments can bound the magnitude of omitted variable bias in complex, nonlinear models.
The abstract discusses parallels between Galois theory and Stone-Weierstrass theorem in various fields.
problem Connecting distinguishing power and expressive power in different fields.
method Elementary theorem connecting distinguishing power and expressive power.
result Foundational principle in linguistics linking distinguishing power and expressive power.
Introduces machine learning basics and algorithms.
problem Developing and analyzing machine learning algorithms.
method Mathematical foundations, optimization, statistical prediction, reproducing kernel theory, Hilbert space techniques, sampling methods, Markov chains, graphical models, variational methods, deep learning, clustering, factor analysis, manifold learning.
result Theoretical support and practical algorithms for machine learning.
Machine learning for many-body physics: efficient solution of dynamical mean-field theorycond-mat.str-el
Machine learning methods for solving the equations of dynamical mean-field theory are developed. The method is demonstrated on the three dimensional Hubbard model. The key technical issues are defining a mapping of an input function to an output function, and distinguishing metallic from insulating solutions. Both meta…
Bridging Algorithmic Information Theory and Machine Learning: A New Approach to Kernel Learningcs.LG
New approach to learning kernels from data using AIT principles.
problem Learning kernels from data in machine learning.
method Sparse Kernel Flows method based on AIT principles.
result Sparse Kernel Flows aligns with MDL principle and offers a robust theoretical foundation.
Advanced Mean Field Theory of Restricted Boltzmann Machinecond-mat.stat-mech
Learning in restricted Boltzmann machine is typically hard due to the computation of gradients of log-likelihood function. To describe the network state statistics of the restricted Boltzmann machine, we develop an advanced mean field theory based on the Bethe approximation. Our theory provides an efficient message pas…
PsychFM predicts individual gambling choices using psychological and machine learning models.
problem Predicting individual gambling choices with high precision.
method PsychFM combines machine learning and psychological theories.
result PsychFM outperforms existing models like random forest and factorization machines.
The study provides a theory for causal machine learning with generalization bounds.
problem Lack of theoretical guarantees for causal machine learning algorithms.
method Introduces a novel change-of-measure inequality to bound model loss.
result Tight bounds on model loss in terms of treatment propensities deviation.
I describe an optimal control view of adversarial machine learning, where the dynamical system is the machine learner, the input are adversarial actions, and the control costs are defined by the adversary's goals to do harm and be hard to detect. This view encompasses many types of adversarial machine learning, includi…
Paper explores alternative cooperative game theory methods for machine learning feature attribution.
problem Debate over Shapley values' relevance in feature attribution.
method Introduces Weber and Harsanyi sets as alternative allocation schemes.
result Provides a coherent framework for designing robust feature attributions.
Quantum models show improved performance in overparameterized regimes.
problem Overfitting in quantum machine learning models.
method Analytical demonstration and numerical experiments on quantum kernel methods.
result Quantum models can operate in the modern, overparameterized regime without overfitting.
The paper outlines future work in random sets theory.
problem Developing a theory of statistical reasoning with random sets.
method Generalizing logistic regression, probability laws, and geometric uncertainty.
result A new geometric approach to uncertainty with general random sets.
Serial problems can't be efficiently parallelized, affecting machine learning models.
problem Inefficiency of parallelization in inherently serial problems.
method Formalized distinction in complexity theory, demonstrated with diffusion models.
result Diffusion models cannot solve inherently serial problems.
Machine learning finds a compact fixed point action for SU(3) gauge theory.
problem Finding accurate and compact parametrizations of fixed point actions for SU(3) gauge theory.
method Used machine learning, specifically a gauge equivariant convolutional neural network.
result Obtained a superior parametrization of a fixed point action for SU(3) gauge theory.
Mixup improves model performance by interpolating random training examples.
problem Overfitting in machine learning models.
method Mixup is a regularization procedure that linearly interpolates random pairs of training examples.
result Mixup works well from a statistical learning theory perspective.
This paper reviews quantum machine learning from NISQ to fault tolerance.
problem The challenges and opportunities in quantum machine learning.
method Comprehensive review of quantum machine learning concepts.
result Coverage of NISQ and fault-tolerant quantum computing approaches.
Develops a new feature theory for robust machine learning.
problem Creating robust machine learning features from training data.
method Stochastic tensor space feature theory with Karhunen-Loeve expansion and hierarchical subspaces.
result Dramatic increases in accuracy for predicting Alzheimer's disease stages.
Machine learning predicts properties of number fields with high accuracy.
problem Predicting properties of algebraic number fields.
method Training machine learning algorithms on various coefficients or polynomials of number fields.
result Machine learning can distinguish between real quadratic fields with high precision and predict properties of Galois extensions.
Improved method for computing Fréchet means on SPD matrices.
problem Computing Fréchet means on the manifold of SPD matrices.
method Random matrix theory-based approach for estimating Fréchet means.
result Significantly outperforms state-of-the-art methods in experiments.
Survey on statistical learning theory for control, focusing on linear systems.
problem Applying machine learning techniques to control systems, especially linear ones.
method Adapting tools from modern high-dimensional statistics and learning theory.
result Recent advances in statistical learning theory for control, particularly for linear systems.
Predicting Properties of Periodic Systems from Cluster Data: A Case Study of Liquid Waterphysics.comp-ph
Machine learning predicts liquid water properties from cluster data.
problem Accuracy of bulk properties from machine-learned potentials is limited by training data.
method Local, atom-centred descriptors enable prediction of bulk properties from cluster data.
result Excellent agreement with experimental and theoretical counterparts of liquid water properties.