This paper makes a small step towards a non-stochastic version of superhedging duality relations in the case of one traded security with a continuous price path. Namely, we prove the coincidence of game-theoretic and measure-theoretic expectation for lower semicontinuous positive functionals. We consider a new broad de…
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48 results for “theoretical”
The paper explores game-theoretic alignment of LLMs with human preferences, finding limitations and conditions.
problem Aligning LLMs with human preferences using game theory.
method Systematic study of payoff choices in a two-player zero-sum game for desirable alignment properties.
result Impossibility of preference matching in game-theoretic LLM alignment under standard assumptions.
New bounds improve generalization in learning scenarios.
problem Limitations of existing information-theoretic bounds in SCO problems.
method Sample-conditioned hypothesis stability and neighboring-hypothesis matrix.
result Sharper generalization guarantees in various learning scenarios.
New bounds show limitations of sample-wise information-theoretic generalization.
problem Limitations of sample-wise information-theoretic generalization bounds.
method Analysis of existing bounds and derivation of new bounds.
result No sample-wise information-theoretic bounds exist for expected squared generalization gap.
Balancing the Scales: A Theoretical and Algorithmic Framework for Learning from Imbalanced Datacs.LG
New framework for learning from imbalanced data with theoretical guarantees.
problem Class imbalance in machine learning, especially in multi-class problems.
method Theoretical framework and new margin loss function for imbalanced classification.
result Proves strong -consistency of the proposed margin loss function.
Information-theoretic Bayesian optimisation techniques have demonstrated state-of-the-art performance in tackling important global optimisation problems. However, current information-theoretic approaches require many approximations in implementation, introduce often-prohibitive computational overhead and limit the choi…
In three-dimensional computational topology, the theory of normal surfaces is a tool of great theoretical and practical significance. Although this theory typically leads to exponential time algorithms, very little is known about how these algorithms perform in "typical" scenarios, or how far the best known theoretical…
Proposes a new theoretical framework for PbRL that requires less human feedback.
problem Lack of theoretical work capturing practical PbRL frameworks.
method Introduces a reward-agnostic PbRL framework that acquires exploratory trajectories before human feedback.
result Demonstrates improved sample complexity for learning optimal policies in linear and low-rank MDPs.
Survey on multiplayer bandits, highlighting theoretical gaps and future directions.
problem Theoretical advancements in multiplayer bandits lack practical implementation in real-world scenarios.
method Organizes and contextualizes existing literature on multiplayer bandits.
result Clear directions for future research in adapting theoretical algorithms to real-world situations.
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.
In this paper we develop some group theoretical methods which are shown to be very useful for a better understanding of the properties of the Riccati equation and we discuss some of its integrability conditions from a group theoretical perspective. The nonlinear superposition principle also arises in a simple way.
Addresses theoretical and practical aspects of Gaussian differential privacy.
problem Theoretical and practical challenges in privacy-preserving data analysis.
method Discussion of f-differential privacy and Gaussian differential privacy.
result Gaussian differential privacy can enhance privacy in various applications.
Theoretical model for iterative user discovery in recommender systems.
problem Iterative feedback loops in recommender systems and their biases.
method Theoretical framework to model system evolution and convergence properties.
result Theoretical bounds and convergence properties on user discovery and blind spots.
We study the task of online boosting--combining online weak learners into an online strong learner. While batch boosting has a sound theoretical foundation, online boosting deserves more study from the theoretical perspective. In this paper, we carefully compare the differences between online and batch boosting, and pr…
In this paper we prove a tertiary index theorem which relates a spectral geometric and a homotopy theoretic invariant of an almost complex manifold with framed boundary. It is derived from the index theoretic and homotopy theoretic versions of a complex elliptic genus and interestingly related with the structure of the…
Empirical study shows consistent meta-RL algorithms adapt to OOD tasks.
problem Theoretical consistency of meta-RL algorithms and its practical implications.
method Empirical investigation of representative meta-RL algorithms, focusing on consistency and adaptation to out-of-distribution tasks.
result Theoretical consistent algorithms can adapt to OOD tasks, while inconsistent ones cannot, but can still fail for poor exploration.
New research shows existing information-theoretic methods can't establish minimax rates for gradient descent in stochastic convex optimization.
problem Establishing minimax rates for gradient descent in stochastic convex optimization using information-theoretic methods.
method Examined several information-theoretic frameworks including input-output mutual information bounds, conditional mutual information bounds, PAC-Bayes bounds, and their variants.
result Proved that none of the examined information-theoretic frameworks can establish minimax rates for gradient descent in stochastic convex optimization.
New tighter bounds for learning algorithms from Steinke & Zakynthinou's supersample setting.
problem Improving generalization bounds for machine learning algorithms.
method Information-theoretic approach using projected loss and Rademacher sequence.
result The new bounds are tighter than previous information-theoretic bounds.
We prove the K-theoretic Farrell-Jones conjecture with (twisted) coefficients for CAT(0)-groups.
M3PO improves model-based meta-RL with theoretical guarantees.
problem Improving sample efficiency in multi-task RL with theoretical guarantees.
method Extending Janner et al. (2019) theorems, proposing M3PO with performance guarantees.
result M3PO outperforms existing methods in continuous-control benchmarks.
We discuss the finite sample theoretical properties of online predictions in non-stationary time series under model misspecification. To analyze the theoretical predictive properties of statistical methods under this setting, we first define the Kullback-Leibler risk, in order to place the problem within a decision the…
This paper explains the theoretical inductive bias of Isolation Forest.
problem Lack of theoretical foundation explaining Isolation Forest's success.
method Formulated the growth process of iForest as a random walk, derived expected depth function using transition probabilities.
result Established a theoretical understanding of iForest's effectiveness and parameter adaptability.
A hybrid impurity measure balances theoretical soundness and computational efficiency.
problem Developing a robust impurity measure for decision trees.
method Integrates Tsallis entropy with an exponential polarization component.
result Simple parametric measures outperform ITC, but ITC variants are competitive with strong theoretical guarantees.
Transfer learning has been proven effective when within-target labeled data is scarce. A lot of works have developed successful algorithms and empirically observed positive transfer effect that improves target generalization error using source knowledge. However, theoretical analysis of transfer learning is more challe…
The paper analyzes LIME for text data and provides theoretical guarantees.
problem LIME's lack of theoretical guarantees in explaining complex models.
method Theoretical analysis of LIME for text data, focusing on decision trees and linear models.
result LIME provides meaningful explanations for simple models like decision trees and linear models.
Improves continual learning with theoretical guarantees and a new algorithm.
problem Learning incremental tasks with dynamic data distributions.
method Contrastive and distillation losses with theoretical performance guarantees.
result Theoretical performance bounds and improved continual learning performance.
Theoretical analysis of deep neural networks for time series data.
problem Theoretical development for deep neural networks on temporally dependent observations is lacking.
method Established non-asymptotic bounds for prediction error of deep neural networks under mixing-type assumptions.
result Deep neural networks can model non-linear time series data with additional logarithmic factors due to dependence.
The Goresky-Hingston coproduct was first introduced by D. Sullivan and later extended by M. Goresky and N. Hingston. In this article we give a Morse theoretic description of the coproduct. Using the description we prove homotopy invariance property of the coproduct. We describe a connection between our Morse theoretic …
The paper explores stability and generalization of deep GCNs.
problem Understanding the stability and generalization of deep GCNs from a theoretical perspective.
method Theoretical analysis of stability and generalization properties of deep GCNs.
result The stability and generalization of deep GCNs are influenced by the maximum absolute eigenvalue of the graph filter operators and the depth of the network.
We prove the K-theoretic Farrell-Jones Conjecture for hyperbolic groups with (twisted) coefficients in any associative ring with unit.
The VAE's reconstruction ability is studied using PAC-Bayes theory.
problem Understanding the performance of VAEs for unseen data.
method PAC-Bayes theory is applied to analyze VAE's reconstruction error.
result Generalization bounds on VAE's reconstruction error are provided.
New model learns from random graph samples to estimate graph parameters.
problem Scalability issues in graph learning methods for large graphs.
method Develops a graph classification model working on randomly sampled subgraphs.
result Validates mini-batch learning on graphs and provides generalization bounds.
Knot-theoretic flocksmath.GT
We characterize the para-associative ternary quasigroups (flocks) applicable to knot theory, and show which of these structures are isomorphic. We enumerate them up to order 64. We note that the operation used in knot-theoretic flocks has its non-associative version in extra loops. We use a group action on the set of f…
Information-theoretic Bayesian regret bounds of Russo and Van Roy capture the dependence of regret on prior uncertainty. However, this dependence is through entropy, which can become arbitrarily large as the number of actions increases. We establish new bounds that depend instead on a notion of rate-distortion. Among o…
Study explores learning behavior of GFlowNets, revealing key mechanisms.
problem Lack of theoretical understanding of GFlowNets' learning dynamics.
method Rigorous theoretical investigation of four dimensions: convergence, sample complexity, implicit regularization, and robustness.
result Elucidates mechanisms underlying GFlowNet's learning dynamics, providing insights into performance factors.
Paper explains why small-loss criterion works for learning from noisy labels.
problem Learning from noisy labels in deep learning with limited labeled data.
method Theoretical analysis and reformulation of the small-loss criterion.
result Theoretical explanation and reformulation of the small-loss criterion.
New method uses dynamic programming for meta continual learning.
problem Challenges of generalization and catastrophic forgetting in sequential learning.
method Developed a theoretical framework using dynamic programming for meta continual learning.
result Theoretical and practical method achieves better accuracy than existing methods.
In PU learning, a binary classifier is trained from positive (P) and unlabeled (U) data without negative (N) data. Although N data is missing, it sometimes outperforms PN learning (i.e., ordinary supervised learning). Hitherto, neither theoretical nor experimental analysis has been given to explain this phenomenon. In …
Softmax Is Not an Artificial Trick: An Information-Theoretic View of Softmax in Neural Networkscs.LG
Despite great popularity of applying softmax to map the non-normalised outputs of a neural network to a probability distribution over predicting classes, this normalised exponential transformation still seems to be artificial. A theoretic framework that incorporates softmax as an intrinsic component is still lacking. I…
Action chunking and data exploration improve behavior cloning in robotics.
problem Exponential errors in learning from demonstrations for continuous control tasks.
method Action chunking and exploratory data collection.
result Control-theoretic stability is key to improving imitation learning.
We integrate information-theoretic concepts into the design and analysis of optimistic algorithms and Thompson sampling. By making a connection between information-theoretic quantities and confidence bounds, we obtain results that relate the per-period performance of the agent with its information gain about the enviro…
Paper analyzes ECE bias and provides bounds for its estimation.
problem Understanding the estimation bias in ECE for machine learning models.
method Information-theoretic approach to analyze bias in uniform mass and uniform width binning strategies.
result Established upper bounds on ECE estimation bias and optimal number of bins.
We study the problem of robust subspace recovery (RSR) in the presence of adversarial outliers. That is, we seek a subspace that contains a large portion of a dataset when some fraction of the data points are arbitrarily corrupted. We first examine a theoretical estimator that is intractable to calculate and use it to …
We present an operator-free, measure-theoretic approach to the conditional mean embedding (CME) as a random variable taking values in a reproducing kernel Hilbert space. While the kernel mean embedding of unconditional distributions has been defined rigorously, the existing operator-based approach of the conditional ve…
In this paper we consider an information theoretic approach for the accounting classification process. We propose a matrix formalism and an algorithm for calculations of information theoretic measures associated to accounting classification. The formalism may be useful for further generalizations and computer-based imp…
New framework evaluates model explanations based on decision task improvement.
problem Evaluation of model explanations often misses practical value.
method Decision-theoretic framework quantifying three key values.
result Provides benchmarks and interprets human-AI decision support.
A framework combines unsupervised and semi-supervised AD using synthetic anomalies.
problem Improving anomaly detection in both unsupervised and semi-supervised settings.
method Proposes a new framework that uses both known and synthetic anomalies for training.
result Synthetic anomalies improve anomaly modeling in low-density regions and provide optimal convergence guarantees.
The Signature Kernelmath.PR
Signature kernel handles sequential data with theoretical and practical advantages.
problem Handling sequential data efficiently and accurately.
method Positive definite kernel based on stochastic analysis with efficient computation.
result Strong empirical performance and theoretical guarantees.