This paper addresses graph embedding issues and introduces \strap for scalable, non-linear embeddings.
problem Preserving out-degree distributions and conflicting optimization goals on directed graphs.
method Introduces transpose proximity and \strap, a factorization-based algorithm that handles both directed and undirected graphs.
result Proposes \strap, which outperforms state-of-the-art methods in effectiveness and scalability.
The paper introduces transposed Poisson superalgebras and their properties.
problem Developing algebraic structures for quantum physics.
method Defining transposed Poisson superalgebras using derivations and proving their identities.
result Six identities are crucial for understanding transposed Poisson superalgebras.
EDAs with matrix transpose improve Bayesian structure learning performance.
problem Improving Bayesian structure learning performance.
method Introducing a matrix transpose mutation operator for EDAs in Bayesian structure learning.
result EDAs with transpose mutation give markedly better performance than conventional EDAs.
Missing data estimation is an important challenge with high-dimensional data arranged in the form of a matrix. Typically this data matrix is transposable, meaning that either the rows, columns or both can be treated as features. To model transposable data, we present a modification of the matrix-variate normal, the mea…
New Sasaki-Einstein 7-spheres found via Berglund-Hübsch transpose.
problem Finding new Sasaki-Einstein 7-spheres.
method Berglund-Hübsch transpose rule applied to Kähler-Einstein 3-folds.
result 75 new Sasaki-Einstein rational homology 7-spheres discovered.
Introduces q-transpose for q-deformed modular group matrices.
problem Understanding q-deformed rational numbers and their properties. method Introduces q-transpose and applies it to refine q-deformed modular group actions. result New proof and refinement of Leclere and Morier-Genoud's trace palindromicity theorem.
We introduce a guide to help deep learning practitioners understand and manipulate convolutional neural network architectures. The guide clarifies the relationship between various properties (input shape, kernel shape, zero padding, strides and output shape) of convolutional, pooling and transposed convolutional layers…
We consider the problem of large-scale inference on the row or column variables of data in the form of a matrix. Often this data is transposable, meaning that both the row variables and column variables are of potential interest. An example of this scenario is detecting significant genes in microarrays when the samples…
Study proposes a more accurate method for classifying transposable elements.
problem Classifying transposable elements for understanding their genetic and evolutionary effects.
method Utilized Support Vector Machines (SVM) for hierarchical classification of transposable elements.
result Proposed a robust approach for hierarchical classification of transposable elements with higher accuracy.
Study explores K-means clustering of variables and its relation to PCA.
problem Exploring the relationship between K-means clustering of variables and PCA.
method Apply PCA to original data and K-means to transposed data, quantify variable contributions to principal components.
result Identifies how variable clusters contribute to principal components identified by PCA.
A new method for higher-order co-occurrences in hypergraphs.
problem Computing higher-order co-occurrences in hypergraphs.
method Face-splitting product or transpose Khatri-Rao product for higher order tuple co-occurrences.
result Demonstrates the utility of the higher order co-occurrence tensor in NLP and hypergraph models.
The Berglund-Hübsch rule connects Calabi-Yau orbifolds to Sasakian manifolds.
problem Connecting Calabi-Yau orbifolds to Sasakian manifolds.
method Applying the Berglund-Hübsch transpose rule to associate Sasaki manifolds.
result Four seven-dimensional Sasakian manifolds of positive Ricci curvature are associated with a K3 orbifold.
Transposable data represents interactions among two sets of entities, and are typically represented as a matrix containing the known interaction values. Additional side information may consist of feature vectors specific to entities corresponding to the rows and/or columns of such a matrix. Further information may also…
Language models fail to process hallucinated responses, and this study diagnoses the failure.
problem Language models fail to process hallucinated responses, leading to over-concentration or diffuse attention.
method The study uses forced scoring of benchmark-labeled responses to compute attention shapes and analyze the symmetric component of the degree-normalized attention operator.
result The study proves that every transpose-invariant spectral diagnostic of the attention operator is orientation-blind and bounds the sensitivity of any Lipschitz diagnostic by the asymmetry coefficient \(G\).
Given a knot and an SL(n,C) representation of its group that is conjugate to its dual, the representation that replaces each matrix with its inverse-transpose, the associated twisted Reidemeister torsion is reciprocal. An example is given of a knot group and SL(3,Z) representation that is not conjugate to its dual for …
New examples show Sasaki manifolds without extremal metrics.
problem Finding Sasaki manifolds without extremal metrics.
method Using Berglund-Hübsch transpose rule and relative K-stability.
result Examples of Sasaki manifolds without extremal metrics.
In machine learning research, the proximal gradient methods are popular for solving various optimization problems with non-smooth regularization. Inexact proximal gradient methods are extremely important when exactly solving the proximal operator is time-consuming, or the proximal operator does not have an analytic sol…
Improves time series classification with forest proximities.
problem Time series classification accuracy and efficiency.
method PF-GAP, an extension of RF-GAP proximities to proximity forests, combined with Multi-Dimensional Scaling and Local Outlier Factors.
result Forest proximities show stronger connection between misclassified points and outliers.
Improved sampling guarantees for weakly log-concave distributions.
problem Sampling from distributions that are not strongly log-concave.
method Proximal sampler with convergence guarantees under weaker assumptions.
result New state-of-the-art sampling guarantees for various target distributions.
Combines gradient-based and competitive learning for unsupervised feature extraction.
problem Handling input data without supervision and replicating input manifold topology.
method Integrates gradient-based and competitive learning approaches to learn topological structures.
result The dual competitive layer outperforms the vanilla layer in high-dimensional datasets.
CFR-Pro enhances treatment effect estimation by incorporating local proximity.
problem Treatment selection bias in HTE estimation from observational data.
method Proximity-enhanced CounterFactual Regression (CFR-Pro) with pair-wise proximity regularizer and subspace projector.
result Significantly outperforms competitors in HTE estimation accuracy.
Improved random forest proximities capture data geometry.
problem Inaccurate random forest proximities do not reflect learned data geometry.
method Introduce RF-GAP: Geometry- and Accuracy-Preserving proximities.
result RF-GAP improves geometric representation in tasks like data imputation.
Introduces PPMM algorithm for nonconvex robust regression problems.
problem Nonconvex tuning-free robust regression problems.
method PPMM algorithm with inner subproblems solved by SSN-PPA.
result Converges to d-stationary point with KL property.
Paper analyzes convergence of proximal algorithm in metric spaces without geodesic convexity.
problem Analyzing convergence of proximal algorithm in general metric spaces.
method Analysis of the Wasserstein proximal algorithm without geodesic convexity assumption.
result Establishes unbiased and linear convergence rate for proximal algorithm under natural Wasserstein inequality.
Extends RF proximities to all supervised distance-based machine learning contexts.
problem Limited utility of RF proximities in various machine learning tasks.
method Introduces generalized Proximity Forest (PF) model and variant for regression.
result Demonstrates unique advantages over RF and k-nearest neighbors models.
Improved bounds for proximal gradient algorithms with computational errors.
problem Analyzing convergence of proximal gradient algorithms with inaccuracies.
method Deriving new tighter deterministic and probabilistic bounds for convex composite problems.
result Probabilistic bounds are more robust and accurate for algorithm verification and performance guarantees.
Paper extends theorem on covering spaces and Jordan curves.
problem Covering and extending theorems for Alexandrov spaces.
method Introduces proximal homotopic cycles to extend the Mitsuishi-Yamaguchi theorem.
result Extensions of the Mitsuishi-Yamaguchi Good Covering Theorem and Jordan curve theorem.
Proximal algorithms applied to current deformation into cycles.
problem Deformation of de Rham currents into cycles.
method Proximal algorithms, total variation denoising for differential forms.
result Calibrated cycles constructed in calibrated manifolds.
Innovative method solves nonconvex optimization on manifolds.
problem Nonconvex optimization problems on Riemannian manifolds.
method Intrinsic Riemannian proximal gradient method.
result Converges for nonconvex or nonembedded problems.
New PnP algorithm converges with relaxed proximal gradient descent.
problem Convergence issues in PnP methods with deep denoisers.
method Relaxed proximal gradient descent for PnP with weakly convex regularization.
result Proposed PnP-αPGD converges for a wider range of regularization parameters. EPINE enhances network embedding by improving adjacency matrix-based high-order proximity.
problem Inaccurate and poorly designed calculation of high-order proximity in network embedding.
method EPINE redefines high-order proximity intuitively and proposes a scalable algorithm for accurate calculation.
result EPINE outperforms existing methods in network reconstruction, link prediction, and node classification.
Stochastic version of proximal distance algorithm analyzed and validated.
problem Optimization of constrained estimation problems.
method Stochastic proximal distance algorithm, with convergence guarantees and finite error bounds.
result Convergence guarantees and finite error bounds for the first time.
This paper studies iteration convergence of Kronecker graphical lasso (KGLasso) algorithms for estimating the covariance of an i.i.d. Gaussian random sample under a sparse Kronecker-product covariance model and MSE convergence rates. The KGlasso model, originally called the transposable regularized covariance model by …
A scalable framework preserves personalized higher-order network proximities.
problem Lack of expressive methods to preserve personalized higher-order network proximities.
method Incorporates random walk into a sound objective to preserve arbitrary higher-order proximities and introduces random walk with restart for personalized-weighted preservation.
result Consistently and substantially outperforms state-of-the-art methods on real-world networks.
This paper extends the Good Covering Theorem and Jordan Curve Theorem for proximal Alexandrov spaces.
problem Extending the Good Covering Theorem and Jordan Curve Theorem to proximal Alexandrov spaces.
method Introducing path cycles and using them to extend the Good Covering Theorem and Jordan Curve Theorem.
result Extensions of the Mitsuishi-Yamaguchi Good Covering Theorem and Jordan Curve Theorem for proximal Alexandrov spaces.
This paper studies fixed sets in ribbon complexes using descriptive proximity spaces.
problem Understanding fixed sets in ribbon complexes within descriptive proximity spaces.
method Introduces descriptive fixed sets and their properties in ribbon complexes, using descriptive proximally continuous maps.
result Establishes that proximal descriptive conjugacy preserves fixed sets in ribbon complexes.
Introduces a new divergence measure for optimal transport.
problem Optimal transport distances and information divergences.
method Infimal convolution formulation of proximal optimal transport divergence.
result Establishes connections to dynamic formulations and partial differential equations.
We propose a new proximal, path-following framework for a class of constrained convex problems. We consider settings where the nonlinear---and possibly non-smooth---objective part is endowed with a proximity operator, and the constraint set is equipped with a self-concordant barrier. Our approach relies on the followin…
Proximal methods avoid local minima in weakly convex problems.
problem Weakly convex optimization problems with strict saddle properties.
method Proximal methods on nonsmooth functions with strict saddle guarantees.
result Proximal methods converge to local minimizers only, when initialized randomly.
Unified framework for training neural networks with non-smooth, non-convex regularizers.
problem Training neural networks with non-smooth, non-convex regularizers.
method ProxGen framework for stochastic proximal gradient descent.
result ProxGen framework achieves the same convergence rate as standard methods and outperforms subgradient-based approaches.
A new method reformulates Optimal Transport Conditional Flow Matching using proximal operators.
problem Optimal Transport Conditional Flow Matching (OT-CFM) for generating models.
method Reformulate OT-CFM using proximal operators and extended Brenier potential.
result OT-CFM dynamics are terminally normally hyperbolic for manifold-supported targets.
SMP model preserves proximity and permutation in graph neural networks.
problem Challenges in graph mining, such as community and leader finding.
method Stochastic Message Passing (SMP) model that maintains proximity and permutation-equivariance.
result SMP model effectively preserves node proximities and permutation-equivariance.
Many machine learning techniques sacrifice convenient computational structures to gain estimation robustness and modeling flexibility. However, by exploring the modeling structures, we find these "sacrifices" do not always require more computational efforts. To shed light on such a "free-lunch" phenomenon, we study the…
Paper relates asymptotic dimension to cofinal dimension using coarse proximities.
problem Relating asymptotic dimension to cofinal dimension in metric spaces.
method Introducing coarse proximities and inverse limit constructions.
result Asymptotic dimension is bounded by coarse cofinal dimension and cofinal dimension of Higson corona.
Proximal Diffusion Models improve generative model efficiency.
problem Improving generative model efficiency and accuracy.
method Developed Proximal Diffusion Models using proximal maps instead of scores.
result Proximal Diffusion Models achieve faster convergence and higher accuracy.
Deep neural networks improve proximal inference for causal effects.
problem Estimating causal effects in the presence of unmeasured confounders.
method Flexible deep neural network to estimate the bridge function.
result Achieves state-of-the-art performance on benchmarks.
In this paper we develop proximal methods for statistical learning. Proximal point algorithms are useful in statistics and machine learning for obtaining optimization solutions for composite functions. Our approach exploits closed-form solutions of proximal operators and envelope representations based on the Moreau, Fo…
Proper proximality proved for various groups on non-positive curvature spaces.
problem Proper proximality of groups acting on non-positive curvature spaces.
method Established proper proximality for groups acting on CAT(0) spaces and hierarchically hyperbolic groups. result Proper proximality of many groups including mapping class groups and subgroups of curve graphs.