In statistical learning, many problem formulations have been proposed so far, such as multi-class learning, complementarily labeled learning, multi-label learning, multi-task learning, which provide theoretical models for various real-world tasks. Although they have been extensively studied, the relationship among them…
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48 results for “learning problems”
Introduces topological deep learning for neural network classification problems.
problem Classifying neural networks using minimal topological structures.
method Formalizes classification problems in a topological setting.
result Demonstrates conditions for the feasibility of classification problems in neural networks.
Efficient strategies for online learning against bandit algorithms solve minimax problems.
problem Solving min-max problems in convex-linear settings with empirical distributions.
method Designing online learning algorithms that play against bandit algorithms, leveraging properties of the set of empirical distributions.
result High-probability convergence guarantees to minimax values for a specific family of sets.
A new optimizer d-AmsGrad improves deep learning for robot learning in non-stationary problems.
problem Noise and outliers in real-world data make deep learning challenging for robot learning.
method Proposed an improved version of AmsGrad optimizer that slowly decays the maximum second momentum to adapt to non-stationary problems.
result The new optimizer outperformed baseline optimizers in robotics problems.
Machine learning models solve inverse eigenvalue problems for symmetric potentials and refractive indices.
problem Solving inverse eigenvalue problems for symmetric potentials and refractive indices.
method Supervised regression models (k-Nearest Neighbours, Random Forests, Multi-Layer Perceptron) trained on eigenvalue datasets.
result Machine learning methods can numerically solve inverse eigenvalue problems under appropriate parameter tuning.
New framework studies policy learning problems under data scarcity.
problem Learning improving policies when data is insufficient.
method Developed a mathematical framework for policy learning problems.
result Reduced policy learning problems to simpler ones in sample complexity.
BackboneLearn speeds up MIO-based machine learning problems.
problem Scaling mixed-integer optimization problems in machine learning.
method An open-source Python framework for MIO problems with indicator variables.
result Solves MIO problems faster and more accurately than existing methods.
Poisson learning doesn't solve graph semi-supervised learning issues.
problem Global information loss in graph-based semi-supervised learning.
method Poisson learning is Laplace regularization with thresholding.
result Poisson learning cannot overcome the global information loss problem.
Machine learning improves solving inverse problems and integrating data.
problem Solving complex inverse problems and integrating data effectively.
method Integrates machine learning techniques with inverse problems and data assimilation.
result Demonstrates machine learning's potential to enhance these fields.
Simulator imperfection, often known as model error, is ubiquitous in practical data assimilation problems. Despite the enormous efforts dedicated to addressing this problem, properly handling simulator imperfection in data assimilation remains to be a challenging task. In this work, we propose an approach to dealing wi…
A new meta-meta classification method tackles few-shot learning tasks.
problem Learning with limited data in small-data settings.
method Designing an ensemble of learners for a large set of problems, then learning how to combine them for a new problem.
result Meta-meta classification outperforms traditional meta-learning and ensembling approaches in one-shot learning tasks.
Learning rate annealing helps even in convex problems, improving generalization.
problem Improving generalization in neural networks, especially convex problems.
method Learning rate annealing schedule (large initial, then small learning rate).
result Gradient descent can reach minima with better generalization using learning rate annealing.
Ranking problems, also known as preference learning problems, define a widely spread class of statistical learning problems with many applications, including fraud detection, document ranking, medicine, credit risk screening, image ranking or media memorability. In this article, we systematically review different types…
We explore the use of deep learning and deep reinforcement learning for optimization problems in transportation. Many transportation system analysis tasks are formulated as an optimization problem - such as optimal control problems in intelligent transportation systems and long term urban planning. Often transportation…
Machine learning reduces combinatorial optimization problem dimensions.
problem Reducing the complexity of large combinatorial optimization problems.
method Generalization of a machine learning model for problem reduction on TSP.
result Machine learning can predict which variables are not part of an optimal solution.
Paper introduces scalable neural architecture for solving NP-hard problems.
problem Solving NP-hard reasoning problems from natural inputs.
method Scalable neural architecture and loss function for discrete Graphical Models.
result Empirically shows efficient learning of NP-hard problems.
Symmetry in inverse problems leads to multiple solutions, but breaking symmetry helps deep learning.
problem Symmetry in physical systems causes multiple solutions in inverse problems, hindering deep learning.
method Careful symmetry breaking on training data helps solve inverse problems and improve deep learning performance.
result Symmetry breaking on training data significantly improves deep learning performance in inverse problems.
Surveying machine learning for solving graph optimization problems.
problem Solving combinatorial optimization problems on graphs requires algorithmic engineering.
method Surveying machine learning approaches for graph optimization.
result Machine learning offers new ways to solve graph optimization problems.
Deep learning solves imaging inverse problems without ground truth.
problem Solving imaging problems without perfect data.
method Taxonomy of deep learning approaches for imaging inverse problems.
result Trade-offs and failure modes identified for different methods.
The paper shows how multi-task learning in neural networks is similar to kernel regression and Hilbert spaces.
problem Understanding the solutions to multi-task shallow ReLU neural network learning problems.
method Analyzing the properties of solutions to multi-task shallow ReLU neural network learning problems, proving uniqueness and equivalence to minimum-norm interpolation problems in Hilbert spaces.
result The solutions to multi-task neural network interpolation problems are almost always unique and coincide with the solution to a minimum-norm interpolation problem in a Sobolev (Reproducing Kernel) Hilbert Space.
Open problem seeks an online learning algorithm for binary classification.
problem Existence of an online learning algorithm for binary classification with sublinear mistakes.
method Assumption of sequence allowing learning algorithm's existence.
result Specific condition determines sequence's learnability.
New adaptive learning rate for FTRL reduces regret to Θ(T^2/3).
problem Minimax regret of Θ(T^2/3) in online learning.
method Adaptive learning rate framework matching stability, penalty, and bias terms.
result Improves Best-of-Both-Worlds (BOBW) regret upper bounds.
Real-world applications often combine learning and optimization problems on graphs. For instance, our objective may be to cluster the graph in order to detect meaningful communities (or solve other common graph optimization problems such as facility location, maxcut, and so on). However, graphs or related attributes ar…
Many important optimization problems, such as the minimum spanning tree and minimum-cost flow, can be solved optimally by a greedy method. In this work, we study a learning variant of these problems, where the model of the problem is unknown and has to be learned by interacting repeatedly with the environment in the ba…
A method learns to solve multilevel combinatorial problems with two players.
problem Multilevel combinatorial optimization problems with multiple players.
method Value-based multi-agent reinforcement learning in a graph neural network framework.
result Close to optimal solutions on graphs up to 100 nodes, with a significant speedup.
We consider the problem of learning a neural network classifier. Under the information bottleneck (IB) principle, we associate with this classification problem a representation learning problem, which we call "IB learning". We show that IB learning is, in fact, equivalent to a special class of the quantization problem.…
Survey of graph learning methods for combinatorial optimization problems.
problem Efficient and effective analysis of graphs for combinatorial optimization problems.
method Two-stage framework: Graph representation learning followed by machine learning.
result Recent studies have shown promise in using machine learning to solve graph-based combinatorial optimization problems.
Adversarial training provides a principled approach for training robust neural networks. From an optimization perspective, adversarial training is essentially solving a bilevel optimization problem. The leader problem is trying to learn a robust classifier, while the follower problem is trying to generate adversarial s…
A novel Federated Learning scheme using Optimal Transport for personalized model training.
problem Training models with data from clients having non-identically distributed data.
method Personalized Federated Learning scheme based on Optimal Transport (FedOT).
result FedOT scheme effectively transfers data from multiple distributions to a common domain and optimizes the prediction model.
Probabilistic learning for binary classification with categorical variables.
problem Binary classification with categorical covariates.
method Probabilistic analysis and two algorithms for learning boolean functions.
result Effective learning of boolean functions from binary data.
Chow and Liu (1968) studied the problem of learning a maximumlikelihood Markov tree. We generalize their work to more complexMarkov networks by considering the problem of learning a maximumlikelihood Markov network of bounded complexity. We discuss howtree-width is in many ways the appropriate measure of complexity and…
Specialized hierarchies improve decision-making by partitioning tasks.
problem Division of labor and specialization in hierarchical systems.
method Information-theoretic on-line learning rule for partitioning tasks.
result Enforces specialization and optimal combination of experts.
In this paper we consider the problem of how a reinforcement learning agent that is tasked with solving a sequence of reinforcement learning problems (a sequence of Markov decision processes) can use knowledge acquired early in its lifetime to improve its ability to solve new problems. We argue that previous experience…
Hardness proven for learning neural networks with polynomial size and Gaussian inputs.
problem Learning one hidden layer ReLU neural networks with polynomial size and Gaussian inputs.
method Based on the hardness of the Continuous Learning with Errors (CLWE) problem.
result Hardness of learning neural networks is proven under standard cryptographic assumptions.
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.
Limits of Transfer Learningstat.ML
New research on limits of transfer learning, proving key selection and dependence requirements.
problem Insufficient theoretical foundation for transfer learning.
method Proved novel results on transfer learning, emphasizing selection of information and dependence between domains.
result Upper bound on improvement possible with transfer learning, highlighting the need for careful selection.
In this paper, we consider unsupervised partitioning problems, such as clustering, image segmentation, video segmentation and other change-point detection problems. We focus on partitioning problems based explicitly or implicitly on the minimization of Euclidean distortions, which include mean-based change-point detect…
The key to success in machine learning (ML) is the use of effective data representations. Traditionally, data representations were hand-crafted. Recently it has been demonstrated that, given sufficient data, deep neural networks can learn effective implicit representations from simple input representations. However, fo…
Self-supervised methods learn from noisy data alone, useful for imaging problems.
problem Inferring signals from noisy and incomplete observations.
method Learning a solver from measurement data alone, without ground-truth references.
result Self-supervised methods can learn meaningful estimates from noisy data.
Study introduces statistical mechanics for min-max problems.
problem Understanding the properties of min-max problems in high dimensions.
method Statistical mechanical formalism for analyzing min-max problems.
result Derives the relationship between training data and generalization error.
ICON learns differential equation operators from prompts, reducing retraining and improving few-shot learning.
problem Training neural networks to solve differential equations without retraining for new problems.
method In-Context Operator Networks (ICON) that learns operators from prompted data and applies them to new problems.
result ICON can generalize to new operators beyond the training distribution and requires only a few demos.
Deterministic Policy Gradient for Learning Equilibrium in Time-Inconsistent Control Problemsq-fin.CP
Develops a reinforcement learning algorithm for learning deterministic equilibrium policies in time-inconsistent control problems.
problem Learning equilibrium policies in time-inconsistent control problems.
method Continuous-time model-free reinforcement learning algorithm using deterministic policy gradient approach.
result Learned equilibrium policies in general time-inconsistent control problems.
The goal of the inverse reinforcement learning (IRL) problem is to recover the reward functions from expert demonstrations. However, the IRL problem like any ill-posed inverse problem suffers the congenital defect that the policy may be optimal for many reward functions, and expert demonstrations may be optimal for man…
Low-rank combinatorial optimization and statistical learning by spatial photonic Ising machinecond-mat.dis-nn
New model enhances SPIM for solving low-rank combinatorial optimization and statistical learning problems.
problem Solving large-scale combinatorial optimization problems efficiently.
method Proposed a new computing model for SPIM that can handle low-rank interaction matrices.
result Demonstrated efficient learning, classification, and sampling of MNIST images using the model.
Sparse Representations, Inference and Learningcond-mat.stat-mech
Statistical physics helps solve complex machine learning problems.
problem Large dimensional inference problems in machine learning.
method Replica symmetric level analysis and cavity methods.
result General framework for solving various problems with weak long-range interactions.
Survey of deep learning methods for inverse problems, highlighting theoretical challenges.
problem Addressing theoretical gaps in deep learning for inverse problems.
method Survey of existing theoretical developments and open problems.
result Highlighting ongoing challenges in deep learning for inverse problems.
Extends GENO framework for GPU optimization of constrained ML problems.
problem Constrained optimization in classical machine learning.
method Extends GENO framework to GPU optimization, specifying problems in a modeling language.
result Solvers on GPU outperform state-of-the-art approaches by several orders of magnitude.
Develops a theory to make learning solutions fair and safe.
problem Ensuring learning solutions are unbiased and safe in critical applications.
method Generates a generalization theory based on PAC learning framework, introduces constrained learning algorithm.
result Proves that constrained learning is as learnable as unconstrained learning, provides practical algorithm.