Bayesian Entropy Neural Networks enforce constraints on deep learning predictions.
problem Deep learning models lack well-defined constraints in their outputs.
method Bayesian Entropy Neural Networks (BENN) using Maximum Entropy principles and the method of multipliers.
result BENN improves model robustness and reliability across various applications.
This work presents entropic constraints from DAGs with hidden variables.
problem Characterizing causal relations in systems with hidden variables.
method Entropic inequality constraints derived from e-separation relations. result These constraints can learn about true causal models from observed data.
The paper calculates bounds for risk metrics and entropies under partial information constraints.
problem Analyzing risk metrics and entropies for unimodal, symmetric distributions with limited information.
method Develops lower and upper bounds for worst-case distortion riskmetrics and weighted entropy for unimodal, symmetric distributions with known mean and variance.
result Sharp upper bounds for distortion riskmetrics and weighted entropy for symmetric distributions.
Improved MESMOC+ optimizes constrained multi-objective problems efficiently.
problem Optimizing constrained multi-objective problems with expensive evaluations.
method Minimizes entropy of Pareto frontier to guide search, using linear cost and decoupled evaluation.
result Significantly faster than alternatives, with more accurate entropy estimation.
A framework estimates categorical distributions under constraints, ensuring generality and uniqueness.
problem Estimating categorical distributions summarizing sample data under marginal constraints.
method Theoretical framework + Iterative Proportional Fitting (IPF) to estimate the distribution.
result A unique categorical distribution of Maximum Entropy under marginal constraints exists and is estimated.
MESMOC optimizes constrained multi-objective problems efficiently.
problem Constrained multi-objective optimization with expensive function evaluations.
method Max-value Entropy Search in the output space.
result MESMOC selects high-quality Pareto solutions efficiently.
Bayesian models use hyperparameters to indirectly assign priors, and this work shows how these priors can be derived from maximum entropy principles.
problem Understanding the assumptions and dependencies in Bayesian hierarchical models.
method Demonstrates how canonical distributions and maximum entropy principles can be used to derive marginal priors in hierarchical models.
result Marginal priors in hierarchical models derived from maximum entropy principles have different constraints compared to the original priors.
Enhances RL by controlling policy stochasticity through trajectory entropy constraints.
problem Non-stationary Q-value estimation and short-sighted entropy tuning in maximum entropy RL.
method Proposes TECRL framework with separate Q-functions for reward and entropy, enforcing a trajectory entropy constraint.
result DSAC-E algorithm achieves higher returns and better stability on OpenAI Gym benchmarks.
Enhances flexibility in data reweighting with optimal transport and maximum entropy principles.
problem Adapting empirical distributions to predefined constraints on moments, tail behavior, etc.
method Nonparametric distributional constraints, maximum entropy principle, optimal transport.
result Maximum entropy weight adjusted empirical distribution close to a specified distribution in optimal transport metric.
We study the problem of discovering the simplest latent variable that can make two observed discrete variables conditionally independent. The minimum entropy required for such a latent is known as common entropy in information theory. We extend this notion to Renyi common entropy by minimizing the Renyi entropy of the …
This work presents PESMOC, Predictive Entropy Search for Multi-objective Bayesian Optimization with Constraints, an information-based strategy for the simultaneous optimization of multiple expensive-to-evaluate black-box functions under the presence of several constraints. PESMOC can hence be used to solve a wide range…
The entropy-degree theorem applies to Alexandrov spaces with curvature constraints.
problem Geometric obstructions and volume bounds in singular spaces.
method Developed new degree theorem for Alexandrov spaces using integral currents.
result Entropy-volume minimization prevents metric singularities in Gromov-Hausdorff limits.
Parallel BO method for multi-objective optimization with constraints.
problem Optimizing multiple objectives under constraints with expensive evaluations.
method PPESMOC, a batch method for simultaneous optimization of black-box functions.
result Empirical evidence shows PPESMOC is effective for multi-objective optimization with constraints.
MGD combines maximum entropy and diffusion methods for efficient sampling.
problem Generating samples from limited information in high dimensions.
method Moment Guided Diffusion (MGD) using stochastic differential equations.
result MGD efficiently samples maximum entropy distributions in finite time.
New method calibrates reference distributions for bounded support.
problem Lack of principled method for bounded-support statistical reference distributions.
method Formulated maximum entropy on projective space of nonnegative measures.
result Prescribed acceptance region uniquely determines deformation parameter.
Unknown constraints arise in many types of expensive black-box optimization problems. Several methods have been proposed recently for performing Bayesian optimization with constraints, based on the expected improvement (EI) heuristic. However, EI can lead to pathologies when used with constraints. For example, in the c…
Uniform entropy bound for Ricci shrinkers with bounded curvature.
problem Bounding entropy for Ricci shrinkers with specific curvature constraints.
method Establishing uniform entropy bounds for simply connected Ricci shrinkers with a finite second homotopy group and uniform curvature bounds.
result Uniform entropy bound for simply connected Ricci shrinkers with a finite second homotopy group and uniform curvature bounds.
The study learns causal graphs from time series data using entropy measures.
problem Learning causal graphs from time series data.
method Constraint-based framework, information-theoretic measures, generalized causation entropy, PC and FCI algorithms.
result The methods effectively construct causal graphs from time series data.
Paper develops MRCs for supervised classification using generalized maximum entropy.
problem Developing robust classifiers for decision problems.
method Generalized maximum entropy principle applied to minimax risk classifiers.
result Learning techniques for determining MRCs with performance guarantees.
Adapting Hedge algorithm for semi-adversarial data with root-entropy regularization.
problem Minimizing regret in prediction with expert advice under varying distributions.
method Follow-the-Regularized-Leader (FTRL) with root-entropy regularization.
result Adaptive minimax optimal regret across all levels of constraint sets.
We introduce a novel Entropy-driven Monte Carlo (EdMC) strategy to efficiently sample solutions of random Constraint Satisfaction Problems (CSPs). First, we extend a recent result that, using a large-deviation analysis, shows that the geometry of the space of solutions of the Binary Perceptron Learning Problem (a proto…
Optimization results are one method for understanding neural computation from Nature's perspective and for defining the physical limits on neuron-like engineering. Earlier work looks at individual properties or performance criteria and occasionally a combination of two, such as energy and information. Here we make use …
Synthesizes sensor likelihoods to enforce accuracy constraints in uncertain systems.
problem Designing sensing architectures for systems with uncertain or unavailable sensor models and accuracy requirements.
method Inverts the design flow, synthesizing measurement likelihoods that minimize Kullback-Leibler divergence from the prior while enforcing an accuracy bound.
result The method synthesizes a maximum-entropy posterior and induced likelihood, accommodating various discrepancy metrics.
Study optimal investment strategies with entropy regularization in volatile markets.
problem Optimal portfolio selection under stochastic volatility with constraints.
method Entropy-regularized relaxed controls, dynamic programming, nonlinear PDEs.
result Existence of classical solutions to nonlinear HJB equation for value function.
Bayesian search optimizes exploration of feasible solutions under expensive constraints.
problem Identifying feasible solutions in computationally expensive constraint spaces.
method Bayesian models with an acquisition function for efficient exploration and exploitation.
result The proposed acquisition function improves the prediction of feasibility.
New algorithm estimates semi-continuous data density using entropy maximization.
problem Estimating density functions for semi-continuous data.
method Maximum entropy principle, requiring only constraint function samples.
result Estimate has significantly less bias compared to existing methods.
Estimates open sets for fibrations, leading to volume vanishing results.
problem Estimating open sets for fibrations.
method Straightforward estimate for open sets with fundamental group constraints.
result Vanishing results for simplicial volume and minimal volume entropy for certain mapping tori.
In this paper we aim to find a measure for the diversity of cash flows between agents in an economy. We argue that cash flows can be linked to probabilities of finding a currency unit in a given cash flow. We then use the information entropy as a natural measure of diversity. This leads to a hirarchical inequality meas…
In the world of modern financial theory, portfolio construction has traditionally operated under at least one of two central assumptions: the constraints are derived from a utility function and/or the multivariate probability distribution of the underlying asset returns is fully known. In practice, both the performance…
Method determines asset prices in incomplete markets to optimize portfolios.
problem Optimizing portfolios in incomplete markets with price constraints.
method Maximum entropy in the mean to adjust distortion function from bid-ask data.
result Prices of assets comply with portfolio optimization constraints.
In this work we present a new method of black-box optimization and constraint satisfaction. Existing algorithms that have attempted to solve this problem are unable to consider multiple modes, and are not able to adapt to changes in environment dynamics. To address these issues, we developed a modified Cross-Entropy Me…
Study finds optimal martingale coupling between two distributions with minimal entropy.
problem Finding the optimal martingale coupling between two distributions with minimal relative entropy.
method Solving a dual problem to find the log-density of the optimal coupling, which represents the marginal and martingale constraints.
result The log-density of the optimal coupling is given by a triplet of real functions representing the marginal and martingale constraints.
Parameter estimation in Markov random fields (MRFs) is a difficult task, in which inference over the network is run in the inner loop of a gradient descent procedure. Replacing exact inference with approximate methods such as loopy belief propagation (LBP) can suffer from poor convergence. In this paper, we provide a d…
Estimate relaxation times in nonextensive systems using gradient flow for Tsallis entropy maximization.
problem Estimating relaxation times in financial market dynamics.
method Developing a method using EGF for maximizing Tsallis entropy.
result Longer relaxation times for nonextensive systems compared to Shannon entropy.
Solves ambiguity in incomplete markets by minimizing price measure entropy.
problem Ambiguity in pricing incomplete markets.
method Minimizes the entropy of the price measure from the economic measure, subject to mark-to-market constraints.
result Resolves ambiguity and provides a consistent pricing measure.
Bayesian optimization (BO) is a model-based approach to sequentially optimize expensive black-box functions, such as the validation error of a deep neural network with respect to its hyperparameters. In many real-world scenarios, the optimization is further subject to a priori unknown constraints. For example, training…
New causal versions of MaxEnt and PIR avoid paradoxical probability updates.
problem Paradoxical probability updates in causal MaxEnt and PIR.
method Separate constraints into cause-specific and mechanism-specific restrictions.
result Causal MaxEnt avoids paradoxical updates and aligns with Information Geometric Causal Inference.
HCLM framework uses entropy regularization for open learning systems.
problem Real-world AI challenges and limitations of deep learning.
method Dynamical and information-theoretic framework with entropy regularization.
result Geometric entropy surrogates, especially log-determinant covariance entropy, induce stronger and more stable information forces.
Develops a new duality between entropy martingale optimal transport and nonlinear pricing-hedging.
problem Entropy Martingale Optimal Transport problem and its associated optimization problem.
method Combines Entropy Optimal Transport and Martingale Optimal Transport theories, with novel penalization terms and constraints.
result Establishes a nonlinear robust pricing-hedging duality, covering various known robust results.
The paper extends entropy maximization to multiscale settings and applies it to neural networks.
problem Achieving optimal risk bounds in neural networks using multiscale entropy.
method Generalizing maximum entropy to multiscale settings and applying it to neural networks.
result The multiscale Gibbs posterior can achieve a smaller excess risk than the single-scale Gibbs posterior in a teacher-student scenario.
In a recent paper, the authors proposed a general methodology for probabilistic learning on manifolds. The method was used to generate numerical samples that are statistically consistent with an existing dataset construed as a realization from a non-Gaussian random vector. The manifold structure is learned using diffus…
Williams and Beer (2010) proposed a nonnegative mutual information decomposition, based on the construction of redundancy lattices, which allows separating the information that a set of variables contains about a target variable into nonnegative components interpretable as the unique information of some variables not p…
The paper studies minimal surface entropy on hyperbolic 3-manifolds and compares it to the hyperbolic case.
problem Minimal surface entropy on hyperbolic 3-manifolds and its comparison to the hyperbolic case.
method Analysis of Ricci flow convergence and comparison of metrics with sectional and scalar curvature constraints.
result The entropy is maximized at the hyperbolic metric under certain curvature conditions.
MIND estimates mutual information from ordinal data without full distributional knowledge.
problem Estimating mutual information from ordinal data with limited data.
method Copula-based maximum-entropy estimation of copula entropies.
result MIND estimator is consistent, data-efficient, and unbounded for any sample size.
The ability of many powerful machine learning algorithms to deal with large data sets without compromise is often hampered by computationally expensive linear algebra tasks, of which calculating the log determinant is a canonical example. In this paper we demonstrate the optimality of Maximum Entropy methods in approxi…
Improved pre-trained embeddings through effective entropy maximization.
problem Developing high-quality pre-trained embeddings for future tasks.
method E2MC criterion defined in terms of low-dimensional constraints.
result Significant improvement in downstream performance.
MaxEnt framework recovers standard model selection procedures and identifies the most generalizable model.
problem Model selection and characterization in data-scientific approaches.
method Starting from linear system of phenomenological constraints, asymptotically derive the distribution over all viable distributions.
result MaxEnt distribution is the most typical among all viable distributions and supports hypothesis testing in a fully-data driven manner.
Econophysics, is based on the premise that some ideas and methods from physics can be applied to economic situations. We intend to show in this paper how a physics concept such as entropy can be applied to an economic problem. In so doing, we demonstrate how information in the form of observable data and moment constra…