Separable losses are inconsistent for structured prediction models.
problem Inconsistency of separable losses in structured prediction models.
method Analysis of separable negative log-likelihood losses for structured prediction.
result Separable losses are not Bayes consistent and may not predict the most probable structure.
The paper introduces toric separable geometries and finds new extremal metrics.
problem Finding explicit extremal Kähler metrics on toric manifolds.
method Introducing toric separable geometries and analyzing their moduli space.
result Explicit computation of scalar curvature and derivation of necessary conditions for extremality.
This work learns sparse tensor representations using mixtures of separable dictionaries.
problem Learning sparse representations of tensor data with structured models.
method Proposes and explores learning a mixture of separable dictionaries with sufficient conditions for local identifiability.
result Developed computational algorithms for batch and online learning.
New algebraic geometry approach to classifying orthogonal separable coordinates.
problem Classifying orthogonal separable coordinates on arbitrary manifolds.
method Algebraic geometric approach using projective varieties and isometry group actions.
result New unexpected structure revealed in well-known classification.
Logarithmic separation profile in hyperbolic groups shows hierarchical structure.
problem Understanding hierarchical structure in hyperbolic groups with logarithmic separation.
method Proving groups with logarithmic separation split over cyclic groups and providing counterexamples.
result Not all groups with hierarchical structure have logarithmic separation profile.
StrADiff separates sources from mixtures without labels, using structured priors.
problem Blind source separation of linear and nonlinear mixtures without labeled data.
method Structured Source-Wise Adaptive Diffusion Framework with Gaussian process priors.
result StrADiff can recover latent source trajectories in an unsupervised manner, especially stable in linear mixtures.
A new method for blind source separation using hierarchical structure and KL divergence.
problem Blind source separation of complex interacting signals.
method Hierarchical log-linear model with KL divergence minimization.
result Superior performance compared to existing techniques on images and time series data.
We solve minimal separator problems in AMP chain graphs and improve structure learning algorithms.
problem Finding minimal separators in AMP chain graphs and learning their structure from data.
method We analyze and solve several versions of the minimal separator problem. We propose modifications to the PC-like algorithm and extend a decomposition-based method for AMP CGs.
result Our modifications of the PC-like algorithm and the LCD-AMP method improve structure learning and are more accurate and stable, especially in high-dimensional settings.
We discuss the polynomial bi-Hamiltonian structures for the Kowalevski top in special case of zero square integral. An explicit procedure to find variables of separation and separation relations is considered in detail.
New algorithm discovers causal relationships in complex data.
problem Discovering causal relationships in data with cycles, latent confounders, and non-linearities.
method Introducing σ-connection graphs and extending σ-separation to handle these complexities.
result First algorithm capable of handling non-linear, cyclic, and latent confounders.
We formalize causal separation in portfolio theory, deriving a closed-form projected Markowitz solution.
problem Portfolio optimization under causal separation conditions.
method Derive a closed-form solution for portfolio optimization using causal separation conditions.
result A closed-form projected Markowitz solution is derived under causal separation conditions.
New PCstar algorithm discovers causal structure of max-linear Bayesian networks.
problem Discovering causal structure in max-linear Bayesian networks due to non-faithfulness.
method PC algorithm modified with C ∗ C^\ast C ∗ -separation assumptions. result PCstar algorithm can orient additional edges not possible with standard PC algorithm.
New graph types help identify complex relationships.
problem Understanding complex relationships in data.
method Introducing separable and essentially separable graphs to characterize and identify graphical models.
result Developed algorithms to identify equivalence classes of essentially separable graphs.
Adaptive method solves saddle point problems with separable structure.
problem Solving saddle point problems with separable structure in machine learning.
method Adaptive stochastic primal-dual coordinate descent with mini-batch updates.
result Adaptive stepsize leads to sharper linear convergence rate.
New upper bound on node count for neural nets to achieve linear separability.
problem Choosing optimal number of nodes and layers for neural nets.
method Derived an upper bound on node count for neural nets with two hidden layers.
result Proved an upper bound that depends on data structure and activation function.
Paper develops robust methods for panel data with latent groups, improving inference under group separation violations.
problem Inference in latent group panel models under group separation violations.
method Selective conditional inference approach to derive conditional distribution of coefficients given estimated group structure.
result Valid inference under violations of group separation, superior to traditional asymptotic methods.
One approach to monitoring a dynamic system relies on decomposition of the system into weakly interacting subsystems. An earlier paper introduced a notion of weak interaction called separability, and showed that it leads to exact propagation of marginals for prediction. This paper addresses two questions left open by t…
Deep learning model separates syntax and semantics for better language generalization.
problem Standard deep learning methods struggle with systematic generalization in natural language.
method Implemented a Syntactic Attention model that separates syntactic and semantic processing.
result The Syntactic Attention model outperforms standard methods on a compositional generalization task.
Suppose that all hyperbolic groups are residually finite. The following statements follow: In relatively hyperbolic groups with peripheral structures consisting of finitely generated nilpotent subgroups, quasiconvex subgroups are separable; Geometrically finite subgroups of non-uniform lattices in rank one symmetric sp…
AR-Flow VAE improves blind source separation with flexible autoregressive priors.
problem Unsupervised blind source separation of latent signals from mixtures.
method AR-Flow VAE uses autoregressive flows to model latent sources, enhancing flexibility and capturing complex dependencies.
result AR-Flow VAE effectively separates latent sources, demonstrating improved performance over conventional methods.
NucleusDiff models atomic nuclei interactions to prevent separation violations in drug design.
problem Maintaining minimum pairwise distance between atoms to avoid separation violations in drug design.
method Enforces distance constraint between atomic nuclei and manifolds in a diffusion model.
result Reduces separation violations by up to 100.00% and enhances binding affinity by up to 22.16%.
This work examines a semi-blind single-channel source separation problem. Our specific aim is to separate one source whose local structure is approximately known, from another a priori unspecified background source, given only a single linear combination of the two sources. We propose a separation technique based on lo…
New separation concepts for Anosov representations help bound Thurston asymmetric metric.
problem Understanding diverging families of Anosov representations.
method Introducing separation concepts and analyzing combinatorial invariants.
result Critical exponent asymptotic to a graph invariant.
Bayesian approach uses generative models as priors for better source separation.
problem Artifacts in source separation for richly structured data.
method Bayesian approach with generative models as priors and noise-annealed Langevin dynamics.
result Achieves state-of-the-art performance for MNIST digit separation.
New algorithm separates vocals from music recordings efficiently.
problem Separate vocal and instrumental parts in music recordings.
method Informed group-sparse representation for linear-time singing voice separation.
result Efficacy confirmed on iKala dataset; music accompaniment follows group-sparse structure.
Efficient neural network for audio source separation.
problem End-to-end general purpose audio source separation.
method SuDoRMRF structure with simple one-dimensional convolutions for feature aggregation.
result SuDoRMRF achieves high quality audio source separation with minimal computational resources.
We show that the orthogonal separation coordinates on the sphere S n S^n S n are naturally parametrised by the real version of the Deligne-Mumford-Knudsen moduli space M ˉ 0 , n + 2 ( R ) \bar M_{0,n+2}(R) M ˉ 0 , n + 2 ( R ) of stable curves of genus zero with n + 2 n+2 n + 2 marked points. We use the combinatorics of Stasheff polytopes tessellating M ˉ 0 , n + 2 ( R ) \bar M_{0,n+2}(R) M ˉ 0 , n + 2 ( R ) t…
The paper proves local laws for non-separable sample covariance matrices.
problem Analyzing non-separable sample covariance matrices with dependent or nonlinearly transformed data.
method Tensor network framework for analyzing fluctuation averaging in the presence of higher-order cumulant structure.
result Optimal averaged local law and full anisotropic local law for non-separable sample covariance matrices.
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.
Unified geometric structure reveals limitations of GANs and proposes geometric GAN.
problem Limitations of existing GAN training methods.
method Unified geometric decomposition of GAN training into three steps: separating hyperplane search, discriminator update, and generator update.
result Geometric GAN converges to Nash equilibrium and outperforms existing methods.
Structured credal learning separates covariate shift and label disagreement.
problem Uncertainty in real-world learning tasks due to covariate shift and noisy labels.
method Introduces a structured credal learning framework that explicitly separates these sources.
result Geometric bounds and decomposition reveal how covariate shifts affect label disagreement contributions.
Framework for lifelong learning of compositional structures.
problem Learning to reuse self-contained chunks of knowledge for novel problems.
method Separates learning into combining existing components and adapting them.
result Framework handles trade-off between stability and flexibility.
Improved mistake bound for group linear separable cases in online multiclass linear classification.
problem Improving mistake bounds for online multiclass linear classification under group linear separable conditions.
method Refined group weak linear separability condition and rational kernel approach.
result Achieved a mistake bound of K ⋅ 2 i l d e O ( 1 / γ log L ) ) K\cdot 2^{ ilde{O}(\sqrt{1/γ}\log L)}) K ⋅ 2 i l d e O ( 1/ γ l o g L ) ) under group weak linear separable condition. We simplify information measure computation using learned features.
problem Computing information measures from raw data is computationally expensive.
method Developed a separable design for computing information measures from learned feature representations.
result A variety of information measures can be computed efficiently through learned feature representations.
Invariant obstructs separating coassociative 4-folds.
problem Obstructing the separation of coassociative 4-folds.
method Defining a Z 2 \mathbb{Z}_2 Z 2 -valued invariant for coassociative 4-folds with spin structures. result Invariant provides an obstruction to separating coassociative 4-folds.
Study reveals structure of local minima in GMMs, identifying key cluster centers.
problem Identifying optimal cluster centers in non-convex GMM landscapes.
method Analyzing the negative log-likelihood function of GMMs in the population limit.
result Local minima share a common structure that partially identifies true cluster centers.
Paper presents a provably correct algorithm for CNMF under separable conditions.
problem Convolutive nonnegative matrix factorization (CNMF) under separable assumptions.
method Algorithm exploiting NMF model and existing separable NMF algorithms.
result Guaranteed solution in low noise settings, runs in polynomial time.
StrEBM learns distinct latent components for better source separation.
problem Blind source separation with identifiable and decoupled latent components.
method Structured latent energy-based model with learnable structural biases.
result The model effectively recovers source components from mixed signals.
New examples show contact invariants can be non-zero even with half Giroux torsion.
problem Understanding contact invariants and their obstructions in 3-manifolds.
method Use bordered contact invariants and innermost contact structures.
result Found closed contact 3-manifolds with non-vanishing contact invariants.
New approach separates VAE and GP for better molecular optimisation.
problem Optimizing complex structured domains like molecular spaces using VAEs.
method Decouples VAE for structure generation and GP for predictive modelling, combining them with a Bayesian update rule.
result Improves identification of high-potential candidates in molecular optimisation.
CASS separates mixed signals using autoencoders and adversarial learning.
problem Separating mixed signals into individual components.
method Cross adversarial source separation via autoencoder framework.
result State-of-the-art performance in separating components with similar data structures.
This paper investigates how data augmentation improves linear separation of manifold data.
problem Understanding how data augmentation enhances linear separation of manifold data.
method Investigates the conditions under which self-supervised representations can linearly separate multi-manifold data.
result Self-supervised learning can linearly separate manifolds with a smaller distance than unsupervised learning.
LOCUS separates brain network connectivity matrices efficiently.
problem High dimensionality, latent sources, and spurious findings in analyzing brain connectivity matrices.
method LOCUS: low-rank structure with uniform sparsity, iterative Node-Rotation algorithm.
result LOCUS achieves more efficient and accurate source separation for connectivity matrices.
This work investigates implicit bias in multiclass separable data using a novel geometry-aware optimizer.
problem Understanding implicit bias in overparameterized models on multiclass separable data.
method Introduces NucGD, a geometry-aware optimizer enforcing low-rank structures through nuclear norm constraints.
result NucGD enables scalable training and characterizes the impact of stochastic optimization dynamics.
New structure on unitary group of Hilbert space.
problem No specific problem stated; constructing a new structure.
method Constructing a Banach Poisson-Lie group structure.
result Banach Poisson-Lie group structure on unitary group of Hilbert space.
Paper distinguishes causal structures under latent confounding and selection bias.
problem Distinguishing causal relationships when latent variables and selection bias are present.
method Formulated selected-marginalized directed graphs (smDGs) to distinguish causal structures.
result Two causal structures are indistinguishable if they have the same selected-marginalized directed graph.
DSGC unifies graph and grid convolutions.
problem Lack of understanding between graph and grid convolutions.
method Depthwise separable graph convolution.
result DSGC outperforms existing methods on benchmark datasets.
We consider the problem of high-dimensional Ising (graphical) model selection. We propose a simple algorithm for structure estimation based on the thresholding of the empirical conditional variation distances. We introduce a novel criterion for tractable graph families, where this method is efficient, based on the pres…