We show how Conway's multivariable potential function can be constructed using braids and the reduced Gassner representation. The resulting formula is a multivariable generalization of a construction, due to Kassel-Turaev, of the Alexander-Conway polynomial in terms of the Burau representation. Apart from providing an …
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48 results for “multivariate representations”
The equivalence between multiportfolio time consistency of a dynamic multivariate risk measure and a supermartingale property is proven. Furthermore, the dual variables under which this set-valued supermartingale is a martingale are characterized as the worst-case dual variables in the dual representation of the risk m…
New algorithms for multivariate RL improve decision-making in complex systems.
problem Complex multi-objective decision-making in reinforcement learning.
method Oracle-free and computationally-tractable algorithms for multivariate distributional RL.
result Convergence rates match scalar reward settings and provide insights into reward dimensionality.
New metric for disentangling multivariate representations, accounting for more complex entanglements.
problem Current disentanglement metrics fail to detect entanglements involving more than two variables.
method Partial Information Decomposition framework to analyze information sharing and propose a new disentanglement metric.
result The proposed metric correctly identifies entanglements in high-dimensional spaces.
We introduce a multivariable Casson-Lin type invariant for links in . This invariant is defined as a signed count of irreducible representations of the link group with fixed meridional traces. For 2-component links with linking number one, the invariant is shown to be a sum of multivariable …
New method interprets multivariate time series for better results.
problem Difficulty in applying traditional methods to multivariate time series.
method Alternative representation of multivariate time series through features.
result Competitive and interpretable results achieved.
Graph-Dictionary model for sparse multivariate signal representation.
problem Capturing complex relational information in multivariate signals.
method Graph dictionaries and bilinear primal-dual splitting algorithm.
result Graph-dictionary model outperforms baselines in signal reconstruction and classification.
Proposes FunNoL for better curve classification and reconstruction in multivariate functional data.
problem Linear methods fail to capture nonlinear structures in multivariate functional data.
method Functional nonlinear learning (FunNoL) method using nonlinear mapping.
result FunNoL outperforms FPCA in curve classification and reconstruction, especially in multivariate settings.
Overcomplete representations and dictionary learning algorithms kept attracting a growing interest in the machine learning community. This paper addresses the emerging problem of comparing multivariate overcomplete representations. Despite a recurrent need to rely on a distance for learning or assessing multivariate ov…
Simplifies study of multivariate shortfall risk measures.
problem Complexity in studying multivariate shortfall risk measures.
method Defines shortfall risk measures through a 1-dimensional function.
result Simplifies properties of multivariate shortfall risk measures.
AdaPTS: Adapting Univariate Foundation Models to Probabilistic Multivariate Time Series Forecastingstat.ML
AdaPTS adapts univariate FMs for multivariate time series forecasting.
problem Challenges in managing feature dependencies and uncertainty quantification in multivariate time series forecasting.
method Adapters that transform multivariate inputs into a latent space and apply univariate FMs independently to each dimension.
result AdaPTS enhances forecasting accuracy and uncertainty quantification compared to baseline methods.
Regularized MFPCA smooths multivariate functional data for clearer patterns.
problem Challenges in controlling roughness of multivariate functional PCs.
method ReMFPCA incorporates a roughness penalty in a penalized framework to smooth PCs.
result Smoothed multivariate functional PCs reveal clearer patterns.
Extremes play a special role in Anomaly Detection. Beyond inference and simulation purposes, probabilistic tools borrowed from Extreme Value Theory (EVT), such as the angular measure, can also be used to design novel statistical learning methods for Anomaly Detection/ranking. This paper proposes a new algorithm based o…
Time series constitute a challenging data type for machine learning algorithms, due to their highly variable lengths and sparse labeling in practice. In this paper, we tackle this challenge by proposing an unsupervised method to learn universal embeddings of time series. Unlike previous works, it is scalable with respe…
In this paper we construct a multivariable link invariant arising from the quantum group associated to the special linear Lie superalgebra sl(2|1). The usual quantum group invariant of links associated to (generic) representations of sl(2|1) is trivial. However, we modify this construction and define a nontrivial link …
Researchers describe unitary representations of mixed braid groups.
problem Understanding unitary representations of mixed braid groups.
method Explicitly describe unitary representations on cohomology of Abelian branched covers.
result Image of the representation is generated by complex reflections and related to the multivariate Burau representation.
Paper addresses the disparity between sampled and mean representations in disentangled learning.
problem Disparity between sampled and mean representations in disentangled learning.
method Proposes a method to eliminate the disparity by proving and utilizing the relationship between total correlation of sampled and mean representations for multivariate normal distributions.
result Demonstrates that a factorized mean representation can have lower total correlation than the sampled representation.
RED CoMETS improves multivariate time series classification accuracy.
problem Complexity of multivariate time series classification.
method Ensemble classifier RED CoMETS for symbolically represented multivariate time series.
result RED CoMETS achieves highest reported accuracy on 'HandMovementDirection' dataset.
We leverage neural networks as universal approximators of monotonic functions to build a parameterization of conditional cumulative distribution functions (CDFs). By the application of automatic differentiation with respect to response variables and then to parameters of this CDF representation, we are able to build bl…
This paper contains an overview of results for dynamic multivariate risk measures. We provide the main results of four different approaches. We will prove under which assumptions results within these approaches coincide, and how properties like primal and dual representation and time consistency in the different approa…
This paper describes a hierarchical learning strategy for generating sparse representations of multivariate datasets. The hierarchy arises from approximation spaces considered at successively finer scales. A detailed analysis of stability, convergence and behavior of error functionals associated with the approximations…
TimeAutoML: Autonomous Representation Learning for Multivariate Irregularly Sampled Time Seriescs.LG
TimeAutoML learns effective representations for irregularly sampled MTS data without manual tuning.
problem Learning effective representations for multivariate time series with irregular sampling rates and variable lengths.
method Autonomous representation learning pipeline with negative sample generation and auxiliary classification task.
result TimeAutoML achieves up to 20% performance improvement in anomaly detection on UCR datasets.
LAVARNET predicts multivariate time series by estimating causal variable relationships.
problem Forecasting multivariate time series requires understanding causal interrelationships among variables.
method LAVARNET is a neural network architecture that estimates causal effects and predicts future values.
result LAVARNET outperforms other models on various real-world data sets.
Kolmogorov neural networks can represent various types of functions.
problem Representing different types of functions with neural networks.
method Continuous, discontinuous bounded or unbounded activation functions in a two hidden layer model.
result Kolmogorov neural networks can represent continuous, discontinuous bounded and all unbounded multivariate functions.
Deep learning models complex multivariate extremes using geometric shapes.
problem Modeling complex extremal dependencies in high-dimensional data.
method Geometric representation and deep learning for flexible semi-parametric models.
result First approach to modeling limit sets using deep learning for high-dimensional data.
Proposes iVDFM for identifying latent factors in multivariate time series.
problem Identifying latent factors in multivariate time series with structural dynamics.
method Identifiable Variational Dynamic Factor Model (iVDFM) with iVAE-style conditioning.
result Identifiable latent factors up to permutation and component-wise affine transformations.
Characterizes symmetric Bernoulli distributions with minimal convex sums.
problem Understanding minimal dependence among Bernoulli random vectors.
method Geometric and algebraic representations of multivariate symmetric Bernoulli distributions.
result Characterizes extremal negative dependence and builds minimal dependence copulas.
MuSiCNet tackles irregularly sampled multivariate time series by treating them as a hierarchy of relatively regular series.
problem Irregularly sampled multivariate time series with missing values.
method Gradual coarse-to-fine approach with multi-scale and multi-correlation attention network.
result MuSiCNet improves ISMTS representation quality through hierarchical learning.
Framework detects anomalies in industrial processes using deep learning.
problem Detect anomalies in complex industrial processes.
method Causal-based framework with unsupervised deep learning.
result Successfully validated abstract contexts of blast furnace assets.
STanHop predicts multivariate time series with memory-enhanced capabilities.
problem Predicting multivariate time series with memory-enhanced capabilities.
method Sparse Tandem Hopfield Network (STanHop) with two external memory modules.
result STanHop outperforms dense Hopfield models in memory retrieval error.
Timely prediction of clinically critical events in Intensive Care Unit (ICU) is important for improving care and survival rate. Most of the existing approaches are based on the application of various classification methods on explicitly extracted statistical features from vital signals. In this work, we propose to elim…
The paper analyzes multivariate Hawkes processes and their induced population processes.
problem Analyzing the time-dependent joint probability distribution of multivariate Hawkes processes.
method Exact and asymptotic analysis of general multivariate Hawkes processes and their induced population processes.
result Full characterization of the time-dependent joint transform of the multivariate population process and its intensity process.
New algorithms for interpreting complex multivariate functions.
problem Hard interpretation of multivariate functions due to many parameters.
method Filtered tensor decompositions of derivative information.
result Nonparametric estimates of smooth decoupled functions.
The paper analyzes multivariate payments in multi-state life insurance using Markovian state processes.
problem Analyzing joint effects of life annuities and death benefits in a multi-state framework.
method Introduces multivariate present value of future payments, derives differential equations and moment generating functions, and focuses on pair-wise covariances.
result Derives Hattendorff type results for pair-wise covariances in a disability model.
A new framework detects anomalies in multivariate time-series data.
problem Lack of explicit relationships between time-series data.
method Graph Attention Network framework that considers temporal and feature dependencies.
result Outperforms state-of-the-art models on three real-world datasets.
Paper introduces MTCM to measure multivariate tail dependence.
problem Classical TDC fails to capture non-exchangeable features of multivariate tail dependence.
method Extends bivariate tail copula measure to multivariate case.
result MTCM reveals off-diagonal stress directions and differences in extremal dependence.
FDApy simplifies analysis of functional data in Python.
problem Analysis of irregularly sampled functional data.
method Implementation of tools for representation, dimension reduction, and dataset generation.
result Efficient analysis of functional data, including irregularly sampled data.
Structured and sparse partial least squares coherence for multivariate cortico-muscular analysisstat.AP
New algorithm extracts shared latent space for cortico-muscular interactions.
problem Challenges of high dimensionality and limited sample sizes in multivariate cortico-muscular analysis.
method Structured and sparse partial least squares coherence (ssPLSC) algorithm.
result ssPLSC achieves competitive or better performance in scenarios with limited sample sizes and high noise levels.
A method for self-supervised learning of multivariate time series data across varying channels.
problem Labeling multivariate biomedical time series data is laborious and expensive.
method Proposes a multi-view self-supervised learning approach using a message passing neural network to extract a single representation across channels.
result Our method, combined with the TS2Vec loss, outperforms all other methods in most settings.
A neural network with a single hidden layer can't represent certain multivariable functions.
problem Representing certain multivariable functions with a neural network having only one hidden layer.
method Developed a continuum version of a one-hidden-layer neural network with ReLU activation, and proved constraints on its parameters and second derivative.
result Existence of a smooth binary function that cannot be precisely represented by any such neural network.
PSEUDo learns patterns in multivariate time series with locality-sensitive hashing and relevance feedback.
problem Efficient pattern detection in large, multi-track sequential data with high variance and lack of ground truth.
method Query-aware locality-sensitive hashing for feature learning, sub-linear training and inference time.
result PSEUDo achieves sub-linear time efficiency for pattern modeling and comparison of 10,000 multivariate time series.
New neural architectures with multivariate nonlinearities are optimal in function space.
problem Optimality of neural architectures with multivariate nonlinearities.
method Construction of Banach spaces via -plane transform and sparsity-promoting norm, proving representer theorem.
result Neural architectures with multivariate nonlinearities are optimal in function space.
Given a set of heterogeneous source datasets with their classifiers, how can we quickly find the most useful source dataset for a specific target task? We address the problem of measuring transferability between source and target datasets, where the source and the target have different feature spaces and distributions.…
Multivariate time series prediction has applications in a wide variety of domains and is considered to be a very challenging task, especially when the variables have correlations and exhibit complex temporal patterns, such as seasonality and trend. Many existing methods suffer from strong statistical assumptions, numer…
BEGIN network models binary data without parametric assumptions.
problem Conditional independence in non-parametric families of binary data.
method BEGIN network models binary data using sparse linear representations and block factorizations.
result BEGIN network captures conditional independence for arbitrary binary and multinomial variables.
The paper proposes a method to estimate latent structures in multivariate data without assuming their existence.
problem Estimating latent structures in multivariate distributions that are difficult to identify and reflect the data generating mechanism.
method A model-free approach using a multiscale nonparametric maximum likelihood estimator.
result The method captures meaningful discrete structure at different scales and integrates them to yield an interpretable discrete representation.
Paper develops heavy-tailed embeddings for better text classification and augmentation.
problem Improving text classification, especially for extreme values.
method Develops heavy-tailed embeddings using multivariate extreme value theory and introduces a scale-invariant classifier.
result The classifier outperforms baselines and generates meaningful augmented text.
Paper extends ICA to ISA with auxiliary variables for better speech representation learning.
problem Learning unsupervised speech representations with independent subspaces.
method Theoretical framework of nonlinear ISA with auxiliary variables.
result Proposes an algorithm to learn speech representations with independent subspaces.