A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
This paper tackles efficient optimization for nonlinear embeddings in similarity learning.
We develop embeddings for nonlinear subspaces preserving vector norms.
The paper analyzes and proposes an algorithm for multi-modal nonlinear embeddings with theoretical performance bounds.
QENDy learns quadratic dynamics from nonlinear systems data.
MMbeddings reduces categorical embeddings by treating them as latent effects, significantly decreasing parameters and mitigating overfitting.
Kernel discriminant analysis uses nonlinear embeddings to improve classification.
InfiniteWalk connects deep network embeddings to spectral graph theory with a nonlinear transformation.
Identifying coordinate transformations that make strongly nonlinear dynamics approximately linear is a central challenge in modern dynamical systems. These transformations have the potential to enable prediction, estimation, and control of nonlinear systems using standard linear theory. The Koopman operator has emerged…
We present several principal bundles of embeddings of compact manifolds (with or without boundary) whose base manifolds are nonlinear Grassmannians. We study their infinite dimensional differential manifold structure in the Fréchet category. This study is motivated by the occurrence of such objects in the geometric Lag…
MCE reduces embedding instability in nonlinear dimensionality reduction.
LNPE enhances local connections in embeddings using extended neighbor propagation.
Stochastic neighbor embedding (SNE) and related nonlinear manifold learning algorithms achieve high-quality low-dimensional representations of similarity data, but are notoriously slow to train. We propose a generic formulation of embedding algorithms that includes SNE and other existing algorithms, and study their rel…
Several popular graph embedding techniques for representation learning and dimensionality reduction rely on performing computationally expensive eigendecompositions to derive a nonlinear transformation of the input data space. The resulting eigenvectors encode the embedding coordinates for the training samples only, an…
Kernel-spectral embedding learns low-dim. structures from noisy data.
A new deep neural network tackles nonlinear functional regression with improved dimensionality reduction.
We introduce a nonlinear method for directly embedding large, sparse, stochastic graphs into low-dimensional spaces, without requiring vertex features to reside in, or be transformed into, a metric space. Graph data and models are prevalent in real-world applications. Direct graph embedding is fundamental to many graph…
DeepEDM forecasts time series by learning dynamics from embeddings.
Meta-learning for Koopman spectral analysis with short time-series data.
New methods for functional data analysis improve manifold methods for continuous data.
Study horizontal discs in fat distributions, proving their existence.
While the existence of low-dimensional embedding manifolds has been shown in patterns of collective motion, the current battery of nonlinear dimensionality reduction methods are not amenable to the analysis of such manifolds. This is mainly due to the necessary spectral decomposition step, which limits control over the…
FREDE efficiently embeds graphs using linear space and guarantees quality.
A method models nonlinear dynamics from data using barycentric coordinates and memory.
Study reveals how manifold geometry impacts linear regression solutions.
The study compares Euclidean and cosine distances in medical drug prescription prediction.
Sensor data analysis plays a key role in health assessment of critical equipment. Such data are multivariate and exhibit nonlinear relationships. This paper describes how one can exploit nonlinear dimension reduction techniques, such as the t-distributed stochastic neighbor embedding (t-SNE) and kernel principal compon…
We construct an algebra of nonlinear generalized tensor fields on manifolds in the sense of J.-F. Colombeau, i.e., containing distributional tensor fields as a linear subspace and smooth tensor fields as a faithful subalgebra. The use of a background connection on the manifold allows for a simplified construction based…
The paper shows how to recover true node positions from a graph or similarity matrix.
Extends importance sampling to nonlinear models using adjoint operators.
This paper lays the foundations for a nonlinear theory of differential geometry that is developed in a subsequent paper which is based on Colombeau algebras of tensor distributions on manifolds. We adopt a new approach and construct a global theory of algebras of generalised functions on manifolds based on the concept …
Recently, some works have suggested methods to combine variational probabilistic inference with Monte Carlo sampling. One promising approach is via local optimal transport. In this approach, a gradient steepest descent method based on local optimal transport principles is formulated to transform deterministically point…
This work connects LLE, factor analysis, and probabilistic PCA through a stochastic perspective.
We examine the algebraic and geometric properties of a uni-directional GRU and word embeddings trained end-to-end on a text classification task. A hyperparameter search over word embedding dimension, GRU hidden dimension, and a linear combination of the GRU outputs is performed. We conclude that words naturally embed t…
Semantic word embeddings represent the meaning of a word via a vector, and are created by diverse methods. Many use nonlinear operations on co-occurrence statistics, and have hand-tuned hyperparameters and reweighting methods. This paper proposes a new generative model, a dynamic version of the log-linear topic model o…
We are concerned with underlying connections between fluids, elasticity, isometric embedding of Riemannian manifolds, and the existence of wrinkled solutions of the associated nonlinear partial differential equations. In this paper, we develop such connections for the case of two spatial dimensions, and demonstrate tha…
We present a new paradigm for speeding up randomized computations of several frequently used functions in machine learning. In particular, our paradigm can be applied for improving computations of kernels based on random embeddings. Above that, the presented framework covers multivariate randomized functions. As a bypr…
A method for estimating nonlinear regression errors and their distributions without performing regression is presented. Assuming continuity of the modeling function the variance is given in terms of conditional probabilities extracted from the data. For N data points the computational demand is N2. Comparing the predic…
New method deflates manifolds to visualize high-dimensional data.
We propose a new method for input variable selection in nonlinear regression. The method is embedded into a kernel regression machine that can model general nonlinear functions, not being a priori limited to additive models. This is the first kernel-based variable selection method applicable to large datasets. It sides…
Locally-contextual CRFs improve sequence labeling performance.
The approximation of nonlinear kernels via linear feature maps has recently gained interest due to their applications in reducing the training and testing time of kernel-based learning algorithms. Current random projection methods avoid the curse of dimensionality by embedding the nonlinear feature space into a low dim…
This paper builds on the theory of generalised functions begun in [1]. The Colombeau theory of generalised scalar fields on manifolds is extended to a nonlinear theory of generalised tensor fields which is diffeomorphism invariant and has the sheaf property. The generalised Lie derivative for generalised tensor fields …
New algorithm learns Koopman operator online, with complexity control and convergence guarantees.
In recent years, deep metric learning has achieved promising results in learning high dimensional semantic feature embeddings where the spatial relationships of the feature vectors match the visual similarities of the images. Similarity search for images is performed by determining the vectors with the smallest distanc…
Researchers solve a complex equation to embed graphs with negative curvature.
The coupled nonlinear volatility and option pricing model presented recently by Ivancevic is investigated, which generates a leverage effect, i.e., stock volatility is (negatively) correlated to stock returns, and can be regarded as a coupled nonlinear wave alternative of the Black-Scholes option pricing model. In this…
A method for learning embeddings from multi-view data using Gromov-Wasserstein.
p-SNE embeds Poisson count data into low dimensions preserving structure.