CANs improve GANs by enforcing structured constraints during training.
problem Generating valid structured objects like molecules and game maps from examples alone.
method Constrained Adversarial Networks (CANs) embed constraints into the model during training, penalizing invalid structures.
result CANs efficiently generate high-quality and novel valid structures.
Graphical notation simplifies complex polynomial constraints in linear models.
problem Complex polynomial constraints in linear structural equation models are impractical.
method Developed a graphical notation to represent these constraints.
result The graphical notation simplifies the representation of many polynomial constraints.
Adversarial constraint learning improves structured prediction with minimal labeled data.
problem Reducing the need for manual label collection in structured prediction tasks.
method Simulates valid structured outputs and trains a model to produce outputs indistinguishable from these simulations using adversarial training.
result The model achieves high accuracy with only a small number of labeled inputs, sometimes requiring none.
Study of motion constraints and path-following on 3D space.
problem Path-following with non-holonomic constraints on R3. method Exploration of geometric structure and construction of guiding vector fields.
result General principles for constructing guiding vector fields for path-following.
The paper tackles hierarchical clustering with structural constraints, providing approximation guarantees and improving upon current techniques.
problem Exploiting prior information in hierarchical clustering for real-world applications.
method Top-down algorithms with provable approximation guarantees, using optimization viewpoint and constraint-based regularization.
result Improved solutions for hierarchical clustering with conflicting prior information.
Adapts Bartnik method to Hilbert manifold structure for vacuum constraint equations.
problem Vacuum constraint equations on compact manifolds of any dimension ≥ 3.
method Adapts Bartnik method to provide Hilbert manifold structure.
result Fibers of scalar curvature and constraint operator are Hilbert submanifolds.
Paper presents a framework to automatically discover constraints from data.
problem Discovering constraints from data for structured output prediction.
method Formulates structured output prediction as ILP, mines constraints by estimating polytopes of feasible set.
result Successfully identifies feasible sets and constraints for various tasks.
Paper tackles graph structure learning via spectral constraints.
problem Learning graphs with specific structures from data.
method Convert structural constraints to Laplacian eigenvalue constraints, integrate with Gaussian graphical modeling.
result Unified framework for learning various graph structures, convergent and scalable.
Geometrically characterizes virtual nonlinear nonholonomic constraints using symplectic methods.
problem Characterizing virtual nonlinear nonholonomic constraints geometrically.
method Geometric characterization using symplectic structures and Chetaev equations.
result A unique control law exists to satisfy virtual constraints, and closed-loop dynamics are projections of uncontrolled dynamics.
MINTS uses a minimalist Bayesian framework to tackle multi-armed bandits with structural constraints.
problem Sequential decision-making under uncertainty with complex structural constraints.
method Minimalist Bayesian framework with profile likelihood to eliminate nuisance parameters.
result MINTS achieves near-optimal regret guarantees and adapts to unimodal structure.
MorphNet automates neural network structure design for resource constraints.
problem Designing efficient neural network structures for resource-limited devices.
method Iteratively shrinks and expands networks using resource-weighted sparsifying regularizers and uniform multiplicative factors.
result Discover novel structures that improve performance while respecting resource constraints.
The paper defines conditions for learning causal graphs from data with unobserved variables.
problem Learning causal graphs from data with unobserved variables.
method Formalizes constraint-based structure learning algorithms under conditions and assumptions.
result Natural family of algorithms output Markov equivalent graphs to the causal graph under faithfulness assumption.
New framework improves reliability of learned representations by modeling uncertainty and structural constraints.
problem Uncertainty in learned representations treated as deterministic, leading to unreliable models.
method Proposes a principled framework for reliable representation learning with uncertainty-aware regularization and structural constraints.
result Improves stability, calibration, and robustness of learned representations.
The paper defines constraints for commuting endomorphisms in generalized tangent bundles.
problem Identifying constraints for commuting endomorphisms in generalized tangent bundles.
method Using Gröbner basis techniques to construct and study tensors forming ideals.
result Explicit construction and study of tensors forming ideals of commuting endomorphisms.
Novel framework for graph learning from data under structural and Laplacian constraints.
problem Graph learning from data under structural and Laplacian constraints.
method Formulation of graph learning problems, probabilistic interpretations, and specialized algorithms incorporating graph Laplacian and structural constraints.
result Experimental results show the proposed algorithms outperform state-of-the-art methods.
Although conservative Hamiltonian systems with constraints can be formulated in terms of Dirac structures, a more general framework is necessary to cover also dissipative systems such as gradient and metriplectic systems with constraints. We define Leibniz-Dirac structures which lead to a natural generalization of Dira…
New method uses algebraic trek criterion for model selection in linear structural equation models.
problem Deciding algebraic equivalence of linear structural equation models.
method Using the half-trek criterion to enumerate and compare constraints.
result Algebraic constraints improve model selection accuracy.
Detects causal scenarios with inequality constraints among classical correlations.
problem Classifying causal structures and identifying those with inequality constraints.
method Using d-separation, e-separation, incompatible supports, and HLP condition.
result Resolved all but three causal scenarios with up to 4 observed variables.
Study reveals structural constraints on income inequality in Latin America.
problem Income inequality in Latin America compared to other economies.
method Product space, Product Gini Index, Xgini coefficient.
result LAC economies are more dependent on products related to high income inequality.
Solvable structures are exploited in order to find families of explicit solutions to evolution PDEs admitting suitable differential constraints. The effectiveness of the method is verified on several explicit examples.
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.
Alternative discrete Dirac mechanics using Dirac structures.
problem Developing a new framework for discrete mechanics.
method Introducing 'continuous Dirac system' and proposing a definition of 'discrete Dirac system'.
result It is possible to recover discrete Lagrangian and Hamiltonian systems.
A new Dirac algebroid approach for nonholonomic systems.
problem Nonholonomic constraints in mechanical systems.
method Developed a Dirac algebroid to generate phase equations for systems with linear nonholonomic constraints.
result Unified approach to describe systems with different potentials.
Characterizes causal structure dominance for latent variables.
problem Determining dominance relations between causal structures with latent variables.
method Complete characterization for three visible variables, partial for four; uses nontrivial inequality constraints.
result Equivalence classes with nontrivial inequality constraints become ubiquitous as the number of visible variables increases.
Paper solves NP-hard projection for three-view cardinality constraints.
problem NP-hard projection onto cardinality constraint sets.
method Formulates projection as linear programming with TVCS.
result Linear programming solution matches original projection.
This paper studies Hamilton-Jacobi equations for magnetic systems with constraints.
problem Understanding dynamics of magnetic systems with geometric constraints.
method Developed Hamilton-Jacobi equations for magnetic systems with nonholonomic constraints.
result Revealed relationships between magnetic structures, constraints, and dynamics.
The paper improves CRFs for logical constraints in structured learning.
problem Structured learning with logical constraints in machine learning.
method General extension of CRF for logical constraints.
result Improved performance on a Document Understanding task.
COSMO learns DAG structure without acyclicity constraints.
problem Learning DAG structure from data efficiently and without constraints.
method Differentiable approximation of smooth orientation matrix.
result COSMO converges to acyclic solutions without evaluating acyclicity.
Constraint-based algorithms often perform worse in terms of accuracy but not speed compared to score-based algorithms.
problem Comparing the performance of constraint-based, score-based, and hybrid algorithms in learning Bayesian network structures.
method Comparison of algorithms using simulated and real-world data, focusing on accuracy and speed.
result Constraint-based algorithms are often less accurate than score-based algorithms but not significantly faster.
Proposes a new algorithm for learning continuous-time Bayesian network structures.
problem Lack of constraint-based algorithms for continuous-time Bayesian networks.
method Develops a constraint-based algorithm using statistical tests for conditional independence.
result The proposed algorithm is more accurate with variables having more than two values.
Reduces Lie (bi-)algebroids and Dirac manifolds using constraint vector bundles.
problem Reduction of Lie (bi-)algebroids and Dirac manifolds.
method Introduces constraint manifolds and constraint vector bundles; proves constraint Serre-Swan theorem; introduces Cartan calculus for constraint forms and multivector fields; shows compatibility with reduction.
result Reduction procedure for Lie (bi-)algebroids and Dirac manifolds.
Study optimal policies under budget and coverage constraints.
problem Optimal policy learning with budget and coverage constraints.
method Combination of knapsack structure, affine threshold rule, linear programming relaxation, Greedy-Lagrangian (GLC), and rank-and-cut (RC) algorithms.
result GLC closely approximates the optimal solution and achieves near-optimal performance in finite samples; RC is approximately optimal under certain conditions.
Paper expands PR to learn constraints for diverse DGMs.
problem Difficult to incorporate structured domain knowledge with DGMs.
method Established mathematical correspondence between PR and RL, and expanded PR to learn constraints as extrinsic reward in RL.
result Models with learned knowledge constraints greatly improve over base generative models.
Privacy constraints affect learning Markov Random Fields differently.
problem Learning Markov Random Fields under differential privacy constraints.
method Algorithms for structure and parameter learning under pure, concentrated, and approximate differential privacy.
result Privacy constraints impose a strong separation between structure and parameter learning in high-dimensional data.
Pluriclosed flow preserves Hermitian-symplectic structures and forms, with topological constraints.
problem Preserving Hermitian-symplectic structures under pluriclosed flow.
method Consideration of an extra evolution equation determined by the Bismut-Ricci form.
result Obtained topological obstruction to long-time existence in arbitrary dimensions.
Develops integrators for nonholonomic systems on Lie groups.
problem Nonholonomic constraints on Lie groups.
method Using retraction maps and Hamel formulation.
result Structure-preserving numerical integrators for nonholonomic systems.
Study discretizes Dirac and port-Hamiltonian systems using manifolds.
problem Discretization of Dirac and port-Hamiltonian systems.
method Retraction and discretization maps on manifolds for Dirac structures, applied to port-Hamiltonian systems.
result Numerical integrators for port-Hamiltonian systems derived from discretization techniques.
Proposes a method to improve hierarchical clustering using set-level structural priors.
problem Lack of supervision for non-leaf structure in hierarchical clustering.
method Introduces set-level structural priors for semi-supervised hyperbolic hierarchical clustering.
result Improves label consistency and similarity-based tree quality over baselines.
Kernel-based L2-boosting with structure constraints improves regression efficiency.
problem Developing efficient kernel methods for regression.
method Kernel-based re-scaled boosting with truncation (KReBooT).
result KReBooT achieves near overfitting resistance and sparse estimates.
SpodNet learns SPD matrices with structural constraints.
problem Estimating SPD matrices with additional structural constraints.
method Introduces SpodNet, a neural network module that guarantees SPD outputs and supports structural constraints.
result SpodNet learns SPD and sparse matrices effectively.
Study rigidifies torus bundles under first Betti number constraints.
problem Understanding the structure of torus fibrations under first Betti number restrictions.
method Established rigidity results and necessary/sufficient conditions for topological splitting.
result Classification of torus bundles under specific Betti number constraints.
The constraints arising from DAG models with latent variables can be naturally represented by means of acyclic directed mixed graphs (ADMGs). Such graphs contain directed and bidirected arrows, and contain no directed cycles. DAGs with latent variables imply independence constraints in the distribution resulting from a…
New method optimizes incentive allocation with budget constraints.
problem Optimizing financial incentives in marketing campaigns with limited feedback.
method Two-step approach: domain adaptation for reward estimation followed by policy optimization.
result Significant improvement in synthetic and real datasets.
Efficient algorithms decide algebraic constraints of causal graphs.
problem Distinguish causal graphs with latent confounders.
method Study algebraic constraints and propose efficient algorithms.
result Decide equivalence or subset of algebraic constraints.
Structured regularizers enable faster optimization on SPD manifolds with constraints.
problem Optimizing SPD matrices with additional constraints.
method Structured regularizers based on symmetric gauge functions.
result Structured regularizers can preserve or induce desirable structure like convexity.
Optimizes bank capital structure under Basel III constraints, simplifying complex dynamics.
problem Optimizing risky investments, dividends, and capital structure under Basel III constraints.
method Formulated as a stochastic control problem, reducing dynamics to a one-dimensional process in leverage ratio.
result Simple policy: pay dividends at an upper barrier and recapitalize at the distress boundary.
Unified framework for structured graph learning from data.
problem Lack of structural knowledge incorporation in graph learning.
method Combining Gaussian graphical models and spectral graph theory, imposing constraints via optimization.
result Provable convergence, computational efficiency, and practical applicability for various graph tasks.
Improved model learns text and hierarchical relations for commonsense knowledge.
problem Predicting hierarchical relations and non-hierarchical knowledge in text data.
method Jointly learns ordering relations and non-hierarchical knowledge from text data. Exploits partial order structure for long-distance triplet constraints.
result Both free text and augmented training constraints improve model performance over baselines.