All knots are fused isotopic to the unknot via a process known as virtualization. We extend and adapt this process to show that, up to fused isotopy, classical links are classified by their linking numbers.
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48 results for “fused links”
Forbidden moves categorify fused links into quivers.
problem Categorify fused links to invariant of links.
method Use forbidden moves to categorify fused links.
result Obtain three polynomial invariants of links.
We construct the complete invariant for fused links. It is proved that the set of equivalence classes of -component fused links is in one-to-one correspondence with the set of elements of the abelization up to conjugation by the elements from the symmetric group .
We consider the group of unrestricted virtual braids, describe its structure and explore its relations with fused links. Also, we define the groups of flat virtual braids and virtual Gauss braids and study some of their properties, in particular their linearity.
Signatures of covering linksmath.GT
The theory of signature invariants of links in rational homology spheres is applied to covering links of homology boundary links. From patterns and Seifert matrices of homology boundary links, an explicit formula is derived to compute signature invariants of their covering links. Using the formula, we produce fused bou…
Predicting missing links via correlation between nodesphysics.soc-ph
As a fundamental problem in many different fields, link prediction aims to estimate the likelihood of an existing link between two nodes based on the observed information. Since this problem is related to many applications ranging from uncovering missing data to predicting the evolution of networks, link prediction has…
The fused lasso penalizes a loss function by the norm for both the regression coefficients and their successive differences to encourage sparsity of both. In this paper, we propose a Bayesian generalized fused lasso modeling based on a normal-exponential-gamma (NEG) prior distribution. The NEG prior is assumed in…
The paper studies algebraic structures related to quantum groups.
problem Understanding centralisers of tensor representations of .
method Introducing fused permutations and braids, proving Schur--Weyl duality, and describing centralisers.
result A conjecture about a generating element of centralisers is proven in some cases.
The solution path of the 1D fused lasso for an -dimensional input is piecewise linear with segments (Hoefling et al. 2010 and Tibshirani et al 2011). However, existing proofs of this bound do not hold for the weighted fused lasso. At the same time, results for the generalized lasso, of which the wei…
The fused lasso is analyzed for high-dimensional piecewise-constant regression coefficients.
problem Estimation of high-dimensional piecewise-constant regression coefficients.
method Formulated a restricted isometry condition for the fused lasso estimator and derived estimation bounds.
result The estimation error can be dominated by either the lasso or the fused lasso rate, depending on the number of non-zero coefficients and piece-wise constant segments.
The Lasso is a very well known penalized regression model, which adds an penalty with parameter on the coefficients to the squared error loss function. The Fused Lasso extends this model by also putting an penalty with parameter on the difference of neighboring coefficients, assuming the…
FUSE neural centrality framework improves data point measurement in high dimensions.
problem Measuring centrality in high-dimensional data is expensive and unstable.
method Combines global and local heads trained on arbitrary representations.
result Reveals meaningful classical ordering and competitive performance.
FUSE improves verification quality without ground truth labels.
problem Verification of model outputs using imperfect judges and reward models.
method Ensembling verifiers without ground truth labels using spectral algorithms.
result FUSE matches or improves upon semi-supervised alternatives in test-time scaling experiments.
Centralisers and Hecke algebras in Representation Theory, with applications to Knots and Physicsmath.RT
The thesis explores centralisers and Hecke algebras in representation theory with applications to knots and physics.
problem Understanding centralisers and Hecke algebras in representation theory.
method Review of classical and quantum Schur-Weyl duality, discussion of quantum groups and their centralisers, and application to knot theory and physics.
result New insights into centralisers and Hecke algebras, leading to solutions for the Yang-Baxter equation and link invariants.
Proposes a method to align Hawkes processes across different event spaces.
problem Aligning Hawkes processes in multiple event spaces.
method Fused Gromov-Wasserstein alignment for Hawkes processes.
result The method effectively aligns Hawkes processes and their event types.
We study the property of the Fused Lasso Signal Approximator (FLSA) for estimating a blocky signal sequence with additive noise. We transform the FLSA to an ordinary Lasso problem. By studying the property of the design matrix in the transformed Lasso problem, we find that the irrepresentable condition might not hold, …
HSIC-based method explains GNN structures.
problem Interpreting GNNs' complex dynamics.
method Flexible model-agnostic explanation using HSIC.
result Identifies crucial structures in GNNs.
Fuses posterior distributions from different datasets using KL divergence.
problem Combining information from multiple datasets with uncertainty.
method Mean field assumption, KL divergence, assign-and-average approach.
result Efficient non-parametric algorithm for fused model computation.
The paper develops estimators for variance in graph structures using fused lasso.
problem Variance estimation in graph-structured problems.
method Developed linear time estimator for homoscedastic case and total variation regularization estimator for heteroscedastic case.
result Minimax rates and consistency for variance estimation in various graph structures.
RFX-Fuse combines Breiman and Cutler's Random Forest with modern ML capabilities.
problem Lack of a unified ML engine with diverse capabilities.
method Unified ML engine with native GPU/CPU support, delivering 5+ functionalities in one model.
result Native explainable similarity and imputation validation.
New autoencoder improves latent space learning by optimizing sliced Gromov-Wasserstein discrepancies.
problem Improving inner discrepancy between prior and posterior distributions in autoencoders.
method Proposed spherical sliced fused Gromov Wasserstein (SSFG) and variants (MSSFG, PSSFG) to find important directions.
result New autoencoders achieve favorable performance in latent manifold learning, image generation, and reconstruction.
Multi-task learning has shown to significantly enhance the performance of multiple related learning tasks in a variety of situations. We present the fused logistic regression, a sparse multi-task learning approach for binary classification. Specifically, we introduce sparsity inducing penalties over parameter differenc…
We propose a new algorithm for solving the graph-fused lasso (GFL), a method for parameter estimation that operates under the assumption that the signal tends to be locally constant over a predefined graph structure. Our key insight is to decompose the graph into a set of trails which can then each be solved efficientl…
Bayesian and POD methods fuse noisy wind tunnel and simulated aerodynamic data.
problem Fusing data from wind tunnel measurements and numerical simulations for accurate aerodynamic modeling.
method Bayesian and Proper Orthogonal Decomposition (POD) methods to infer true aerodynamic fields.
result Bayesian method is more robust with scarce data and accounts for uncertainties.
Estimating the Number of Components in Finite Mixture Models via the Group-Sort-Fuse Procedurestat.ME
New method estimates mixture model components efficiently.
problem Estimating the number of components in finite mixture models.
method Group-Sort-Fuse (GSF) procedure for simultaneous estimation of order and mixing measure.
result GSF achieves consistent estimation of true mixture order and convergence rate.
Bayesian model fuses diverse microbiome data types.
problem Challenges in fusing different types of microbiome data.
method Flexible multinomial-Gaussian generative model with variational EM algorithm.
result Inferred latent variables provide common dimensionality reduction and predictive posterior distribution.
We propose a tensor-based model that fuses a more granular representation of user preferences with the ability to take additional side information into account. The model relies on the concept of ordinal nature of utility, which better corresponds to actual user perception. In addition to that, unlike the majority of h…
DoRA improves adaptation efficiency for large models by factoring norms and fusing kernels.
problem High-rank DoRA is computationally expensive and infeasible on common GPUs.
method Factored norms and fused Triton kernels to reduce memory and speed up computation.
result Fused implementation is up to 2.0x faster for inference and 1.9x faster for gradient computation.
M2VN forecasts financial volatility by fusing time series data with news embeddings.
problem Forecasting financial volatility with unstructured news data.
method Combines deep neural networks with open-source market features and news embeddings.
result M2VN outperforms existing models in financial volatility forecasting.
Fused Encoder Networks improve momentum strategies on crypto data.
problem Deploying momentum strategies on crypto data with limited samples leads to over-fitted models.
method Hybrid transfer learning model combining source and target datasets.
result Fused Encoder Networks outperform classical momentum strategies and benchmarks.
Diversity or complementarity of experts in ensemble pattern recognition and information processing systems is widely-observed by researchers to be crucial for achieving performance improvement upon fusion. Understanding this link between ensemble diversity and fusion performance is thus an important research question. …
We present the group fused Lasso for detection of multiple change-points shared by a set of co-occurring one-dimensional signals. Change-points are detected by approximating the original signals with a constraint on the multidimensional total variation, leading to piecewise-constant approximations. Fast algorithms are …
Paper introduces a novel framework for supervised graph prediction using Optimal Transport.
problem Supervised labeled graph prediction.
method Fused Gromov-Wasserstein (FGW) loss and FGW barycenter with neural network weights and learned graphs.
result The method can interpolate in the labeled graph space and achieve good performance on difficult problems.
Enhances graph comparison by incorporating edge features using Fused Gromov-Wasserstein distance.
problem Graph distances overlook edge attributes, limiting their effectiveness.
method Introduced Fused Gromov-Wasserstein distance for graph comparison with edge features. Proposed algorithms for distance and barycenter computation.
result Empirically validated the effectiveness of the novel distance in graph learning tasks.
RDL-Net improves speech enhancement with fewer parameters and better performance.
problem Improving speech enhancement with fewer parameters and better performance.
method Proposes RDL-Net, a CNN combining residual and dense aggregations without over-allocating parameters.
result RDL-Net achieves higher speech enhancement performance with fewer parameters and lower computational requirements.
We study regularized estimation in high-dimensional longitudinal classification problems, using the lasso and fused lasso regularizers. The constructed coefficient estimates are piecewise constant across the time dimension in the longitudinal problem, with adaptively selected change points (break points). We present an…
ESE-FN improves elderly activity recognition accuracy.
problem Recognizing individual actions and human-object interactions in elderly activities.
method Exploits multi-modal features from RGB videos and skeleton sequences using ESE attentions and a new Multi-modal Loss.
result ESE-FN achieves best accuracy on ETRI-Activity3D dataset.
ABM automates feature engineering and variable selection for loss-based models.
problem Improving model performance through better feature engineering and variable selection.
method ABM uses group and fused lasso regularization to automatically select cutting points and variables.
result ABM integrates feature engineering, variable selection, and model training.
Proposes a method to improve regression model performance with limited target data using fused-regularizer.
problem Model shifts and covariate shifts in high-dimensional regression.
method Two-step method with fused-regularizer to leverage source data for target task.
result Robust to covariate shifts, minimax-optimal under certain conditions, and validated by numerical tests.
MCFNet recovers spatial detail and fuses it with semantic information for real-time segmentation.
problem Recovering spatial detail information and fusing it with semantic information in real-time.
method Proposes a new architecture (MCFNet) with feature refinement and fusion modules, and a gating unit.
result Achieves competitive performance with high speed (75.5% mIOU, 151.3 FPS on Cityscapes).
Fused Lasso Additive Modelstat.ME
We consider the problem of predicting an outcome variable using covariates that are measured on independent observations, in the setting in which flexible and interpretable fits are desirable. We propose the fused lasso additive model (FLAM), in which each additive function is estimated to be piecewise constant…
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…
Framework optimizes expensive manufacturing processes efficiently.
problem Optimizing input parameters for advanced manufacturing methods.
method Bayesian optimization with tailored acquisition function and parallel acquisition.
result Framework efficiently finds optimal parameters with minimal process cost.
ScoreFusion fuses multiple diffusion models to enhance generative modeling of a target population.
problem Enhancing generative modeling of a target population with limited data.
method ScoreFusion uses KL barycenters of auxiliary populations and recasts the learning problem as score matching in denoising diffusion.
result ScoreFusion achieves a dimension-free sample complexity bound in total variation distance.
A new estimator reduces bias and improves efficiency for staggered adoption studies.
problem Bias in difference-in-differences estimates for staggered adoption studies.
method Fused Extended Two-Way Fixed Effects (FETWFE) estimator with automatic parameter selection.
result FETWFE identifies correct restrictions with probability tending to one, improving efficiency.
Kernel fusion is a popular and effective approach for combining multiple features that characterize different aspects of data. Traditional approaches for Multiple Kernel Learning (MKL) attempt to learn the parameters for combining the kernels through sophisticated optimization procedures. In this paper, we propose an a…
AdaTrans: Feature-wise and Sample-wise Adaptive Transfer Learning for High-dimensional Regressionstat.ML
AdaTrans adapts to feature and sample transfer in high-dimensional regression.
problem High-dimensional linear regression with more features than samples.
method F-AdaTrans and S-AdaTrans methods using fused-penalties and adaptive weights.
result AdaTrans achieves convergence rates close to oracle estimators and near-minimax optimal rates.
This work proposes a novel autoencoder for fusing visible and infrared images.
problem Challenging task to combine spatial and spectral information from visible and infrared images.
method Spatially constrained adversarial autoencoder with residual architecture and adversarial regularizer.
result Generates a more realistic fused image with enhanced spatial and spectral information.