Archetypal analysis represents a set of observations as convex combinations of pure patterns, or archetypes. The original geometric formulation of finding archetypes by approximating the convex hull of the observations assumes them to be real valued. This, unfortunately, is not compatible with many practical situations…
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48 results for “Archetypes”
Archetypal analysis is a data decomposition method that describes each observation in a dataset as a convex combination of "pure types" or archetypes. These archetypes represent extrema of a data space in which there is a trade-off between features, such as in biology where different combinations of traits provide opti…
Sparse NMF with archetypal regularization aims to robustly represent data points.
problem Representing data points as sparse linear combinations of archetypes.
method Sparse NMF with archetypal regularization, introducing strong and weak robustness.
result Theoretical robustness guarantees hold under minimal assumptions.
In this paper, we introduce an unsupervised learning approach to automatically discover, summarize, and manipulate artistic styles from large collections of paintings. Our method is based on archetypal analysis, which is an unsupervised learning technique akin to sparse coding with a geometric interpretation. When appl…
Develops a Riemannian archetypal analysis for interpretable non-linear data.
problem Limited performance of classical archetypal analysis on non-linear data.
method Riemannian geometry for data-driven pullback, geodesic convex combinations, convex relaxation followed by non-convex refinement.
result Combines interpretability of classical archetypal analysis with expressive power of modern non-linear models.
"Deep Archetypal Analysis" generates latent representations of high-dimensional datasets in terms of fractions of intuitively understandable basic entities called archetypes. The proposed method is an extension of linear "Archetypal Analysis" (AA), an unsupervised method to represent multivariate data points as sparse …
The paper proves consistency of archetypal analysis for multivariate data.
problem Finding optimal archetype points for multivariate data.
method Uses convex polytope to summarize data, proving consistency under specific distribution assumptions.
result Archetype points converge to optimal solution under certain conditions.
Paper introduces probabilistic methods to approximate archetypal analysis, reducing complexity.
problem Inherent computational complexity of archetypal analysis limits its practical applicability.
method Two preprocessing techniques: dimensionality reduction and representation cardinality reduction, using probabilistic geometry.
result The method effectively reduces scaling and provides near-optimal solutions for prediction errors.
Wasserstein archetypal analysis finds optimal data summaries using Wasserstein metric.
problem Finding optimal data summaries using Wasserstein metric.
method Alternative formulation of archetypal analysis based on Wasserstein metric, with regularization and gradient-based computational approach.
result Existence and consistency of solutions for the regularized problem.
Proposes Fair Archetypal Analysis to reduce fairness concerns in data representation.
problem Inadvertent encoding of sensitive attributes in Archetypal Analysis.
method Integrates fairness regularization into Archetypal Analysis and its nonlinear extension.
result Reduces group separability without significantly compromising explained variance.
AA extracts archetypes from data for clear feature extraction.
problem Non-convex optimization problem in AA.
method Computational procedure extracting archetypes as convex combinations of data.
result AA offers interpretable representations for high-dimensional data.
Given a collection of data points, non-negative matrix factorization (NMF) suggests to express them as convex combinations of a small set of `archetypes' with non-negative entries. This decomposition is unique only if the true archetypes are non-negative and sufficiently sparse (or the weights are sufficiently sparse),…
We revisit a pioneer unsupervised learning technique called archetypal analysis, which is related to successful data analysis methods such as sparse coding and non-negative matrix factorization. Since it was proposed, archetypal analysis did not gain a lot of popularity even though it produces more interpretable models…
Archetype and archetypoid analysis can be extended to functional data. Each function is represented as a mixture of actual observations (functional archetypoids) or functional archetypes, which are a mixture of observations in the data set. Well-known Canadian temperature data are used to illustrate the analysis develo…
New binary AA methods improve on existing techniques.
problem Binary data limitations in AA methods.
method Proposed two optimization frameworks for binary AA.
result Superior performance on synthetic and real binary data.
New method for selecting clusters in residential electricity data.
problem Selecting useful clusters in electricity consumption data.
method Formalizing expert knowledge as external validation measures.
result Successfully reconstructed customer archetypes.
Bayesian framework learns latent preference archetypes for many-objective optimization.
problem Expanding space of trade-offs and context-dependent human values.
method Dirichlet-process mixture model for latent preference archetypes, hybrid queries for efficient information.
result Mixture-aware Bayesian optimization outperforms standard methods on synthetic and real-world benchmarks.
The emergence of a concept in shallow neural networkscond-mat.dis-nn
RBMs learn archetypes when trained on blurred copies of them, revealing a critical sample size.
problem Determining the critical sample size for RBMs to learn archetypes.
method Formal equivalence between RBMs and Hopfield networks, statistical-mechanics of disordered systems, Monte Carlo simulations.
result A phase diagram highlights regions where learning can be accomplished.
This research categorizes AMM designs for secure token exchanges.
problem Designing AMMs for cryptoeconomic systems can lead to financial risks and inefficiencies.
method Developed an AMM taxonomy and proposed three archetypes.
result AMM archetypes meet key requirements for token issuance and exchange.
Prototypal analysis is introduced to overcome two shortcomings of archetypal analysis: its sensitivity to outliers and its non-locality, which reduces its applicability as a learning tool. Same as archetypal analysis, prototypal analysis finds prototypes through convex combination of the data points and approximates th…
Non-Negative Matrix Factorization, NMF, attempts to find a number of archetypal response profiles, or parts, such that any sample profile in the dataset can be approximated by a close profile among these archetypes or a linear combination of these profiles. The non-negativity constraint is imposed while estimating arch…
Archetypal analysis approximates data by means of mixtures of actual extreme cases (archetypoids) or archetypes, which are a convex combination of cases in the data set. Archetypes lie on the boundary of the convex hull. This makes the analysis very sensitive to outliers. A robust methodology by means of M-estimators f…
A federated model learns shared archetypes from heterogeneous clients in continual learning.
problem Federated learning struggles with client heterogeneity and streaming distribution shifts.
method Clients encode their data as low-rank Hebbian operators, which are sent to a central server for aggregation and factorization into global archetypes.
result Improved global archetype reconstruction and associative retrieval in heterogeneous clients, drift, and novelty settings.
Paper introduces SMM for forecasting multiple time series with missing values.
problem Forecasting multiple time series with missing and noisy values.
method Sliding Mask Method (SMM) using Non-negative Matrix Factorization (NMF).
result The method outperforms state-of-the-art methods in time series forecasting.
Extends multidimensional scaling to analyze three-way asymmetric proximities.
problem Analyzing asymmetric and three-way proximities in a Euclidean space.
method Unified h-plot methodology for three-way asymmetric proximities, including symmetric and conditional frameworks.
result Identification of archetypal profiles and clustering structures.
Here are considered some categorical aspects of "Differential calculus" archetype of local approximation of arbitrary morphisms by "linear" ones.
Archetypal analysis is an exploratory tool that explains a set of observations as mixtures of pure (extreme) patterns. If the patterns are actual observations of the sample, we refer to them as archetypoids. For the first time, we propose to use archetypoid analysis for binary observations. This tool can contribute to …
Nonnegative matrix factorization (NMF) is a widely used linear dimensionality reduction technique for nonnegative data. NMF requires that each data point is approximated by a convex combination of basis elements. Archetypal analysis (AA), also referred to as convex NMF, is a well-known NMF variant imposing that the bas…
NOTMAD estimates context-specific Bayesian networks without breaking datasets.
problem Non-convexity of acyclic graphs limits sharing information between context-specific estimators.
method NOTMAD models context-specific Bayesian networks as mixtures of archetypal DAGs, estimating structures and parameters jointly.
result NOTMAD shares information between context-specific acyclic graphs, enabling single-sample resolution.
GraphHull models networks with clear multi-scale explanations of community structure.
problem Lack of self-explainable models in graph machine learning.
method Two-level convex hulls with global archetypes and local prototypes.
result GraphHull models networks with clear multi-scale explanations.
We develop a Chern character map for twisted equivariant non-abelian cohomology.
problem Understanding non-abelian cohomology theories and their applications.
method General construction of the Chern character map for twisted equivariant non-abelian cohomology.
result Illustrated the construction by computing the equivariant Sullivan model of Cohomotopy.
Biarchetype analysis identifies extreme instances of observations and features.
problem Representing complex data structures in a more interpretable form.
method Solves biarchetype analysis through an algorithm that identifies biarchetypes as mixtures of observations and features.
result Biarchetypes enhance interpretability of data structures compared to traditional methods.
Expectation Propagationstat.ML
Variational inference is a powerful concept that underlies many iterative approximation algorithms; expectation propagation, mean-field methods and belief propagations were all central themes at the school that can be perceived from this unifying framework. The lectures of Manfred Opper introduce the archetypal example…
Be Water: An Evolutionary Proof for Trend-Followingphysics.soc-ph
Trend-following strategies outperform in a noisy financial market, mirroring ancient wisdom.
problem Navigating the complex, noisy financial market environment.
method Agent-based model with 10,000 agents representing different trading strategies.
result Trend-following strategies are structurally more robust than mean-reversion strategies.
Clusters cryptocurrency market states via cross correlation analysis.
problem Analyse cryptocurrency market dynamics.
method Cross correlation structure analysis over 5 years.
result Cryptocurrency market clusters into 4 states.
This article introduces a universal moduli space for the set whose archetypal element is a pair that consists of a metric and second fundamental form from a compact, oriented, positive genus minimal surface in some hyperbolic 3-manifold. This moduli space is a smooth, finite dimensional manifold with canonical maps to …
A new framework separates classifier calibration and discrimination.
problem Combining reliability and resolution in probabilistic predictions.
method Manokhin Probability Matrix separates reliability and resolution using Spiegelhalter Z-statistic and AUC-ROC.
result Classifiers are categorized into four archetypes: Eagle, Bull, Sloth, and Mole.
Schrödinger Manifoldsmath-ph
This article propounds, in the wake of influential work of Fefferman and Graham about Poincaré extensions of conformal structures, a definition of a (Poincaré-)Schrödinger manifold whose boundary is endowed with a conformal Bargmann structure above a non-relativistic Newton-Cartan spacetime. Examples of such manifolds …
Locally adapted parameterizations of a model (such as locally weighted regression) are expressive but often suffer from high variance. We describe an approach for reducing the variance, based on the idea of estimating simultaneously a transformed space for the model, as well as locally adapted parameterizations in this…
The study classifies and imitates trading agents in financial markets.
problem Classifying and imitating trading agents in continuous double auctions.
method Developed an agent-based model for trading, applied opponent modeling for classification, and used behavioral cloning for imitation.
result Techniques for classification and imitation were experimentally compared and evaluated.
This study analyzes financial equity research reports to identify frequently asked questions and automates 80% of them.
problem Insufficient empirical analysis of questions answered in financial equity research reports.
method Analyzed 72 financial equity research reports, classifying sentences into 169 unique question archetypes. Used public corporate reports to classify questions' potential for automation.
result Approximately 80% of financial equity research reports can be automated, with 78.7% of questions automatable.
New method uses neural networks for better financial hedging.
problem Spanning multi-asset payoffs with vanilla options.
method One-hidden-layer feedforward neural networks for numerical solution.
result Better hedging results with neural networks compared to single-asset approaches.
Despite being originally inspired by the central nervous system, artificial neural networks have diverged from their biological archetypes as they have been remodeled to fit particular tasks. In this paper, we review several possibilites to reverse map these architectures to biologically more realistic spiking networks…
In most illiquid markets, there is no obvious proxy for the market price of an asset. The European corporate bond market is an archetypal example of such an illiquid market where mid-prices can only be estimated with a statistical model. In this OTC market, dealers / market makers only have access, indeed, to partial i…
The Wasserstein distance received a lot of attention recently in the community of machine learning, especially for its principled way of comparing distributions. It has found numerous applications in several hard problems, such as domain adaptation, dimensionality reduction or generative models. However, its use is sti…
Optimal Dimensionality Reduction of Complex Dynamics: The Chess Game as Diffusion on a Free Energy Landscapephysics.data-an
Dimensionality reduction is ubiquitous in analysis of complex dynamics. The conventional dimensionality reduction techniques, however, focus on reproducing the underlying configuration space, rather than the dynamics itself. The constructed low-dimensional space does not provide complete and accurate description of the…
ESNs with transfer learning predict long-term chaotic patterns in spatiotemporal dynamical systems.
problem Predicting long-term statistical patterns of spatiotemporally chaotic dynamical systems.
method Echo state networks (ESNs) with transfer learning.
result ESNs with transfer learning accurately predict long-term statistical properties of spatiotemporally chaotic PDEs.
Many models of market dynamics make use of the idea of conservative wealth exchanges among economic agents. A few years ago an exchange model using extremal dynamics was developed and a very interesting result was obtained: a self-generated minimum wealth or poverty line. On the other hand, the wealth distribution exhi…