PathRank ranks paths in spatial networks using multi-task learning.
problem Ranking paths in spatial networks for better navigation services.
method Data-driven framework using multi-task learning, spatial network embedding, and recurrent neural networks.
result PathRank effectively ranks paths based on historical trajectories.
Connectivity proven in large rank Gromov boundary of free factor complex.
problem Connectivity of Gromov boundary in large rank free factor complex.
method Analyzing Gromov boundary and free factor complex properties.
result Gromov boundary is path connected and locally path connected in large rank.
MixPath unifies multi-path neural architecture search with one-shot training.
problem Efficiently searching multi-path neural architectures.
method One-shot multi-path supernet with Shadow Batch Normalization (SBN).
result SBN stabilizes optimization and improves ranking performance.
This work proposes a hybrid method for error detection in noisy Knowledge Graphs.
problem Error detection in noisy Knowledge Graphs.
method Hybrid and modular approach combining path ranking and representation learning.
result Hybrid method outperforms individual methods on benchmarks and real-world dataset.
Evaluates explanations of LTR models using decision paths and compares their accuracy.
problem Challenges in evaluating local explanations of LTR models due to lack of ground truth feature importance scores.
method Focuses on tree-based LTR models, extracts ground truth feature importance scores using decision paths, and compares them with explanation techniques.
result Explanation accuracy varies depending on the model and data point.
Study path geometries with constant torsion and cone structures.
problem Characterizing path geometries with nontrivial torsion.
method Introducing constant torsion, establishing correspondence with cone structures, describing in terms of integrable systems.
result Path geometries with constant torsion correspond to cone structures on homogeneous ruled surfaces.
Inf-FS selects features by graph paths, ranking them for infinite feature sets.
problem Feature selection in large datasets with relevance and redundancy.
method Graph-based feature selection with infinite paths, evaluating feature subsets using matrix power series and Markov chains.
result Inf-FS outperforms other methods in various feature selection scenarios.
We propose a sparse and low-rank tensor regression model to relate a univariate outcome to a feature tensor, in which each unit-rank tensor from the CP decomposition of the coefficient tensor is assumed to be sparse. This structure is both parsimonious and highly interpretable, as it implies that the outcome is related…
Predictive models learned from historical data are widely used to help companies and organizations make decisions. However, they may digitally unfairly treat unwanted groups, raising concerns about fairness and discrimination. In this paper, we study the fairness-aware ranking problem which aims to discover discriminat…
Solar algorithm selects variables faster and more accurately in high-dimensional data.
problem Variable selection in high-dimensional data with high accuracy and stability.
method Subsample-ordered least-angle regression (solar) and its coordinate descent generalization (solar-cd) using L0 norm solution path averaging. result Solar selects variables with high accuracy and stability, reducing redundant variable selection.
In this article, we derive a Bayesian model to learning the sparse and low rank PARAFAC decomposition for the observed tensor with missing values via the elastic net, with property to find the true rank and sparse factor matrix which is robust to the noise. We formulate efficient block coordinate descent algorithm and …
Study on positivity properties of vector bundle Monge-Ampère equation.
problem Analyzing positivity in vector bundle Monge-Ampère equation.
method Investigates MA-positivity and MA-semi-positive solutions for different ranks of holomorphic bundles over complex surfaces and manifolds.
result Positivity preservation in rank-two holomorphic bundles but not in higher ranks.
Paper introduces HRPCFD for efficient training of stochastic processes.
problem Discontinuities in stochastic processes over time.
method High Rank Path Development method and HRPCFD metric.
result Efficient algorithm for training HRPCFD from data.
Researchers find optimal paths on a specific geometric group.
problem Finding optimal paths on a Cartan group with a sub-Finsler quasimetric.
method Using the Pontryagin Maximum Principle in coordinates of the first kind.
result They found extremals for arbitrary left-invariant sub-Finsler quasimetrics.
Proposes a method to balance fairness and utility in ranking models.
problem Systematic disparity across protected groups in ranking models.
method Model-agnostic post-processing framework using dynamic programming.
result Achieves a balance between fairness and utility across various metrics and datasets.
iSplit LBI predicts individualized partial rankings from ties, outperforming state-of-the-art methods.
problem Predicting partial rankings from pairwise comparisons with ties, considering individual preferences.
method Variable splitting-based algorithm (iSplit LBI) that generates a sequence of estimations with a regularization path, decomposing parameters into abnormal signals, personalized signals, and random noise.
result iSplit LBI significantly outperforms state-of-the-art alternatives in predicting individualized partial rankings.
Develops methods to find most probable paths on complex manifolds.
problem Identifying optimal paths for manifold-valued processes, especially those with non-trivial structures.
method Constructs a general approach to defining and identifying most probable paths by measuring the Onsager-Machlup function on the anti-development of such processes.
result Derives explicit equations for development most probable paths that encompass various manifold-valued processes.
We develop the geometry of folding paths in Outer space and, as an application, prove that the complex of free factors of a free group of finite rank is hyperbolic.
Study shows almost complex structures with certain tensor properties are prevalent.
problem Characterizing almost complex structures with specific tensor properties.
method Analyzes the space of almost complex structures on compact manifolds.
result The space of almost complex structures with rank at least k Nijenhuis tensor is either empty or dense in each component.
We consider small-time asymptotics for diffusion processes conditioned by their initial and final positions, under the assumption that the diffusivity has a sub-Riemannian structure, not necessarily of constant rank. We show that, if the endpoints are joined by a unique path of minimal energy, and lie outside the sub-R…
We consider efficient implementations of the generalized lasso dual path algorithm of Tibshirani and Taylor (2011). We first describe a generic approach that covers any penalty matrix D and any (full column rank) matrix X of predictor variables. We then describe fast implementations for the special cases of trend filte…
The paper examines ellipticity of specific equations on vector bundles.
problem Investigating ellipticity of vector bundle versions of Monge-Ampère equations.
method Analyzing continuity paths and preserving ellipticity of equations.
result Not all equations preserve ellipticity along continuity paths, but σ2 does. Researchers found optimal paths on a specific geometric group.
problem Finding optimal paths in a geometric group with a sub-Finsler metric.
method Used Pontryagin Maximum Principle for time-optimal control problem.
result Found extremals for left-invariant sub-Finsler metric.
New method adapts neural networks without losing prior knowledge.
problem Understanding and enabling flexible adaptation of neural networks.
method Differential geometry framework, functionally invariant paths (FIP).
result Achieves comparable state-of-the-art performance on continual learning and sparsification tasks.
An almost complex structure J on a 4-manifold X may be described in terms of a rank 2 vector bundle E. A splitting of J consists of a pair of line bundles spanning E. A hypersurface M in X satisfying a nondegeneracy condition inherits a CR-structure from J and a path geometry from the splitting. Using the Cartan-Kähler…
We present evolution equations for a family of paths that results from anisotropically weighting curve energies in non-linear statistics of manifold valued data. This situation arises when performing inference on data that have non-trivial covariance and are anisotropic distributed. The family can be interpreted as mos…
Generative model for TPPs using signatures and distributional discrepancies.
problem Limitations of signature methods for TPPs and lack of global sequence-level loss in neural models.
method Introduce interarrival embedding to lift jump paths to continuous paths of bounded variation, enabling signature methods for discrete event sequences. Develop sigTPP, a signature-based generative model trained on path-level loss.
result sigTPP achieves the best average rank across multiple metrics and outperforms or is within a standard error of the strongest baseline in 64% of dataset-metric pairs.
In this note, we present a new way to associate a spectral triple to the noncommutative C∗-algebra C∗(Λ) of a strongly connected finite higher-rank graph Λ. We generalize a spectral triple of Consani and Marcolli from Cuntz-Krieger algebras to higher-rank graph C∗-algebras C∗(Λ), and we prove that these s…
Estimates roughness of financial volatility paths using horizontal visibility graphs.
problem Estimating roughness in financial volatility models.
method Introduces L+(t) for first-passage horizons, treating uncensored observations as first-passage times.
result Estimates roughness through a single tail exponent θ, separating rough Bergomi volatility from classical models.
Paper simplifies calculating causation probabilities and ranks root causes.
problem Computational challenges in assessing causal relationships.
method Algorithmic simplifications and novel methodological framework for Root Cause Analysis.
result Significantly reduces computational complexity for calculating causation probabilities.
LSDAT reduces query efficiency for decision-based adversarial attacks.
problem Improving query efficiency for decision-based adversarial attacks.
method Low-rank and sparse decomposition (LSD) to craft perturbations.
result LSDAT achieves superior fooling rates with fewer queries.
Scalable machine learning with path signatures for time series and graphs.
problem Challenges in real-world time series and graph data.
method Combines rough path theory with probabilistic, deep, and kernel methods.
result Scalable models for time series and graph data.
Given a smooth manifold M and a totally nonholonomic distribution Δ⊂TM of rank d, we study the effect of singular curves on the topology of the space of horizontal paths joining two points on M. Singular curves are critical points of the endpoint map F:γ↦γ(1) defined on the space Ω of horizonta…
For a connected locally path-connected topological space X and a continuous function f on it such that its Reeb graph Rf is a finite topological graph, we show that the cycle rank of Rf, i.e., the first Betti number b1(Rf), in computational geometry called \emph{number of loops}, is bounded from above by …
Boosting as gradient descent algorithms is one popular method in machine learning. In this paper a novel Boosting-type algorithm is proposed based on restricted gradient descent with structural sparsity control whose underlying dynamics are governed by differential inclusions. In particular, we present an iterative reg…
Spirals are not shortest paths in certain sub-Riemannian geometries.
problem Nonminimality of spiral-like curves in sub-Riemannian manifolds.
method Construction of a competing curve to demonstrate non-minimality.
result Spiral-like curves are not length minimizing in sub-Riemannian manifolds.
Gaussian graphical models are semi-algebraic subsets of the cone of positive definite covariance matrices. Submatrices with low rank correspond to generalizations of conditional independence constraints on collections of random variables. We give a precise graph-theoretic characterization of when submatrices of the cov…
LR-EDNN reduces PDE solver complexity by limiting network weights to low-rank subspace.
problem Efficiently solving time-dependent PDEs with deep neural networks.
method Low-rank constraint on network weights using SVD for efficient parameter updates.
result LR-EDNN achieves comparable accuracy to full EDNN with fewer parameters and lower cost.
The Lasso is a very well known penalized regression model, which adds an L1 penalty with parameter λ1 on the coefficients to the squared error loss function. The Fused Lasso extends this model by also putting an L1 penalty with parameter λ2 on the difference of neighboring coefficients, assuming the…
E-commerce sponsored search contributes an important part of revenue for the e-commerce company. In consideration of effectiveness and efficiency, a large-scale sponsored search system commonly adopts a multi-stage architecture. We name these stages as ad retrieval, ad pre-ranking and ad ranking. Ad retrieval and ad pr…
Signature portfolios approximate optimal wealth in non-Markovian markets.
problem Approximating optimal wealth in non-Markovian markets.
method Linear path-functional portfolios based on signatures of market weights.
result Signature portfolios can uniformly approximate any continuous portfolio function.
The space of matrices of positive determinant GL^+_n inherits an extrinsic metric space structure from R^{n^2}. On the other hand, taking the infimum of the lengths of all paths connecting two points in GL^+_n gives an intrinsic metric. We prove bilipschitz equivalence for intrinsic and extrinsic metrics on GL^+_n, exp…
New method generates synthetic time series paths with more flexibility.
problem Restrictions in generating synthetic paths using Brownian reference.
method Introduces Triangular-Reference Schrödinger Bridges (TR-SBTS) for time series generation.
result Generates synthetic paths with more flexibility in stochastic volatility and correlated noise.
This expository monograph cuts a short path from the common, elementary background in geometry (linear algebra, vector bundles, and algebraic ideals) to the most advanced theorems about involutive exterior differential systems: (1) The incidence correspondence of the characteristic variety, (2) Guillemin normal form an…
The optimal ranking score between precision and recall is rarely F1 and can be found using specific methods.
problem Finding a meaningful and optimal compromise between precision and recall scores.
method Established a shortest path between precision- and recall-induced rankings, framed the problem as an optimization problem, and provided theoretical tools to find the optimal β.
result F1 and its skew-insensitive version are not optimal tradeoffs between precision and recall scores.
The paper connects neural collapse and low-rank bias in networks with L2 regularization.
problem Understanding the emergence of low-rank bias and neural collapse in L2-regularized networks.
method Unified theoretical framework linking TCV and rank of weight matrices, proving global optimality of DNC1, and establishing a benign landscape property.
result Zero TCV across intermediate layers minimizes representation cost under natural architectural constraints, and DNC1 is globally optimal.
The paper describes distances on Sol-type groups using novel geometric techniques.
problem Understanding distances on Sol-type groups.
method New technique of Euclidean curve surgery to describe uniformly roughly geodesic paths.
result The rough isometry type of distances on Sol-type groups is determined by a specific metric restriction.
FAIRY explains user actions and social media feeds.
problem Users struggle to understand why certain items appear in their social feeds.
method FAIRY uses an interaction graph to model user behavior and ranks feed items, scoring paths connecting user actions and feed items.
result FAIRY provides clear explanations for user actions and feed items, enhancing transparency and user understanding.