A new framework for information theory considers computational constraints.
problem Understanding information in complex systems with computational limitations.
method Variational extension of Shannon's information theory with computational constraints.
result Predictive V-information can be created through computation and reliably estimated from data. The paper extends utility maximization by integrating partial information and robust VaR constraints.
problem Optimal investment under partial information and robust VaR-type constraints.
method Combines partial information and robust regulatory constraints (VaR) to solve the utility maximization problem.
result Optimal wealth is a decreasing function of state price density, and depends on the overall evolution of the estimated market price of risk.
New algorithm clusters data and learns kernels without relaxing constraints.
problem Learning kernels or distance metrics from pairwise constraints without losing generalization.
method Joint clustering and kernel learning without relaxing constraints.
result Outperforms existing approaches on diverse datasets.
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.
Hierarchical clustering is a popular unsupervised data analysis method. For many real-world applications, we would like to exploit prior information about the data that imposes constraints on the clustering hierarchy, and is not captured by the set of features available to the algorithm. This gives rise to the problem …
Proposes SPCA to incorporate structural constraints in model identification.
problem Model identification with partial structural knowledge.
method Structural Principal Component Analysis (SPCA) that leverages structural information.
result Demonstrates improved model estimates using synthetic and industrial data.
Many machine learning approaches are characterized by information constraints on how they interact with the training data. These include memory and sequential access constraints (e.g. fast first-order methods to solve stochastic optimization problems); communication constraints (e.g. distributed learning); partial acce…
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…
Study portfolio optimization with partial info and drawdown constraints using deep learning.
problem Optimizing portfolios with partial information and maximum drawdown constraints.
method Bayesian framework, dynamic programming, semi-explicit solutions, deep learning for stochastic control.
result Numerical solutions and performance analysis with deep learning, convergence to Merton problem.
New method uses logical relations to derive bounds and inequality constraints from causal models.
problem Recovering bounds and inequality constraints from unobserved confounding.
method Using rules of probability and restrictions on counterfactuals implied by causal graphical models.
result Powerful method to recover known and novel bounds and constraints.
We use the LMO invariant to find constraints for a knot to admit a purely or reflectively cosmetic surgery. We also get a constraint for knots to admit a Lens space surgery, and some information for characterizing slopes.
Safe Bayesian optimization method using information theory.
problem Optimizing unknown functions while respecting safety constraints.
method Information-theoretic exploration criterion for continuous domains.
result The method learns the value of the safe optimum up to arbitrary precision.
Paper improves deep learning for solving evolutionary equations with trainable hard constraints.
problem Low computational accuracy of standard PINNs in large temporal domains.
method Sequential learning strategies and trainable influence functions for hard constraints.
result Significantly improved computational accuracy and universality of the method.
Embedding models, which learn latent representations of users and items based on user-item interaction patterns, are a key component of recommendation systems. In many applications, contextual constraints need to be applied to refine recommendations, e.g. when a user specifies a price range or product category filter. …
New algorithms for efficient causal interventions with budget constraints and without constraints.
problem Efficiently learning best interventions in causal graphs with budget constraints.
method Developed algorithms for both budgeted and non-budgeted causal bandits, optimizing regret and side-information usage.
result Proposed algorithms minimize cumulative regret and perform better than standard methods.
Physics-informed neural networks improve by measuring effective dimensionality of constraints.
problem Task interference in physics-informed neural networks due to shared parameter space.
method Introduce effective dimensionality (deff) as an operator invariant to quantify constraints. result Effective dimensionality measures unconstrained parameter directions, independent of network architecture.
New constraints on space and adaptivity in bandits force more batches and memory use.
problem Simultaneous space and adaptivity constraints in stochastic bandits.
method Proved lower bounds and constructed an algorithm with near-minimax regret.
result Near-minimax regret requires more batches and memory than previously thought.
Unified physics-informed learning method improves generalization performance.
problem Lack of theoretical analysis for hybrid settings with incomplete physical constraints.
method Unified residual form unifying collocation and variational methods, establishing generalization performance governed by affine variety dimension.
result Generalization performance is determined by affine variety dimension, not just the number of parameters.
The paper develops methods for time-varying constrained online convex optimization.
problem Time-varying loss and constraint functions in online convex optimization.
method Model-based augmented Lagrangian methods (MALM) for time-varying and delayed feedback.
result Sublinear regret and constraint violation for both time-varying and delayed feedback scenarios.
Survey of Gaussian process constraints for modeling expensive data.
problem Modeling expensive data with physical constraints.
method Overview of various Gaussian process constraints and their implementation.
result Discussion of computational challenges introduced by constraints.
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.
Paper resolves open problems on sample complexity in binary hypothesis testing.
problem Open problems in distributed simple binary hypothesis testing under information constraints.
method One-shot lower bound on Bayes error, streamlined sample complexity formula, reverse data-processing inequality.
result Optimally tight sample complexity bounds for communication-constrained simple binary hypothesis testing.
In this work we consider adversarial contextual bandits with risk constraints. At each round, nature prepares a context, a cost for each arm, and additionally a risk for each arm. The learner leverages the context to pull an arm and then receives the corresponding cost and risk associated with the pulled arm. In additi…
This paper proposes an active metric learning method for clustering with pairwise constraints.
problem Clustering with pairwise constraints and improving clustering performance.
method Active metric learning method that queries informative instance pairs and updates the learned metric sequentially.
result The proposed method enhances clustering performance and provides a tighter error bound.
Existing information-theoretic frameworks based on maximum entropy network ensembles are not able to explain the emergence of heterogeneity in complex networks. Here, we fill this gap of knowledge by developing a classical framework for networks based on finding an optimal trade-off between the information content of a…
Study market efficiency under partial information using SDEs and optimization.
problem Market efficiency under partial information constraints.
method McKean-Vlasov-type SDEs, Wasserstein barycenters, KL divergence, convex optimization, optimal control, nonlinear filtering.
result Convergence of reduced-information market price processes to true price process under increasing information flow.
New method finds balanced clusters in graphs using auxiliary information.
problem Finding balanced clusters in graphs with population-level constraints.
method Proposes individual-level balancing constraint and develops spectral clustering algorithms.
result Establishes first statistical consistency result for constrained spectral clustering.
Information-theoretic bounded rationality describes utility-optimizing decision-makers whose limited information-processing capabilities are formalized by information constraints. One of the consequences of bounded rationality is that resource-limited decision-makers can join together to solve decision-making problems …
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.
We present an objective function for learning with unlabeled data that utilizes auxiliary expectation constraints. We optimize this objective function using a procedure that alternates between information and moment projections. Our method provides an alternate interpretation of the posterior regularization framework (…
Improved method using filtered PDEs for robust physics-informed deep learning.
problem Complex real-world problems with noisy and sparse data.
method Proposed a surrogate constraint (FPDE) to filter and reduce the influence of noisy and sparse observation data.
result FPDE models converge better and produce higher quality solutions with less data.
Optimizes SGLD noise structure for better generalization bounds.
problem Improving generalization bounds for large models trained with SGLD.
method Manipulates the noise structure in SGLD to optimize information-theoretical bounds.
result Optimal noise covariance is the square root of the expected gradient covariance under certain constraints.
This paper introduces a new member of the family of Variational Autoencoders (VAE) that constrains the rate of information transferred by the latent layer. The latent layer is interpreted as a communication channel, the information rate of which is bound by imposing a pre-set signal-to-noise ratio. The new constraint s…
Data processing inequalities link Fisher information to local differential privacy constraints.
problem Understanding how Fisher information scales with local differential privacy constraints.
method Developed data processing inequalities for Fisher information under local differential privacy.
result Implications for private estimation with optimal bounds and error rates.
Most existing distance metric learning methods assume perfect side information that is usually given in pairwise or triplet constraints. Instead, in many real-world applications, the constraints are derived from side information, such as users' implicit feedbacks and citations among articles. As a result, these constra…
Travel decisions tend to exhibit sensitivity to uncertainty and information processing constraints. These behavioural conditions can be characterized by a generative learning process. We propose a data-driven generative model version of rational inattention theory to emulate these behavioural representations. We outlin…
Bayesian method estimates dynamics from near-optimal trajectories.
problem Estimating dynamics from near-optimal expert trajectories in reinforcement learning.
method Constraint-based Bayesian approach integrating expert near-optimality.
result Significant improvements in decision-making and transfer success.
This study analyzes communication constraints in MoE architectures using information theory.
problem Communication constraints in Mixture-of-Experts (MoE) architectures.
method Developed a rate-distortion characterization of finite-rate gating in MoE architectures using information theory.
result Yielded capacity-aware limits for communication-constrained MoE systems.
Bayesian algorithms improve crowdsourcing with label and instance constraints.
problem Efficiently labeling large datasets with additional human annotator information.
method Developed Bayesian algorithms for semi-supervised crowdsourced classification under label and instance constraints.
result Improved performance compared to unsupervised crowdsourcing on various datasets.
We consider the problem of sequential sampling from a finite number of independent statistical populations to maximize the expected infinite horizon average outcome per period, under a constraint that the expected average sampling cost does not exceed an upper bound. The outcome distributions are not known. We construc…
Most of metric learning approaches are dedicated to be applied on data described by feature vectors, with some notable exceptions such as times series, trees or graphs. The objective of this paper is to propose a metric learning algorithm that specifically considers relational data. The proposed approach can take benef…
As one of the most important types of (weaker) supervised information in machine learning and pattern recognition, pairwise constraint, which specifies whether a pair of data points occur together, has recently received significant attention, especially the problem of pairwise constraint propagation. At least two reaso…
We present an information-theoretic framework for solving global black-box optimization problems that also have black-box constraints. Of particular interest to us is to efficiently solve problems with decoupled constraints, in which subsets of the objective and constraint functions may be evaluated independently. For …
New IBOs resolve contradictions in mutual information optimization.
problem Contradictions in mutual information optimization between IBP, PIBP, and recent results.
method Formulated and optimized variational bounds on new IBOs.
result New IBOs account for parameter selection in trained models.
Study on collaboration vs. independent data collection in sensor networks.
problem Impact of sensor correlation on data collection strategies.
method Analysis of Fisher information and Cramer-Rao bound.
result Optimal strategy involves transferring non-immediate information for improved estimation.
First-order method solves stochastic bilevel optimization with linear constraints.
problem Stochastic bilevel optimization with linear constraints and noise.
method Developed a novel framework using gradient-based techniques and smoothed penalty functions.
result Achieved finite-time convergence guarantees for (δ,ε)-Goldstein stationary points. In typical applications of Bayesian optimization, minimal assumptions are made about the objective function being optimized. This is true even when researchers have prior information about the shape of the function with respect to one or more argument. We make the case that shape constraints are often appropriate in at…
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.