Unsupervised Learning of Density Estimates with Topological Optimization
Kernel density estimation is a key component of a wide variety of algorithms in machine learning, Bayesian inference, stochastic dynamics and signal processing. However, the unsupervised density estimation technique requires tuning a crucial hyperparameter: the kernel bandwidth. The choice of bandwidth is critical as it controls the bias-variance trade-off by over- or under-smoothing the topological features. Topological data analysis provides methods to mathematically quantify topological characteristics, such as connected components, loops, voids et cetera, even in high dimensions where visualization of density estimates is impossible. In this paper, we propose an unsupervised learning approach using a topology-based loss function for the automated and unsupervised selection of the optimal bandwidth and benchmark it against classical techniques -- demonstrating its potential across different dimensions.
Code (0)
등록된 구현이 없습니다.
Tasks
Density EstimationBayesian InferenceSimilar Papers 제목 키워드 기반
Autoregressive Models: What Are They Good For?
Autoregressive (AR) models have become a popular tool for unsupervised learning, achieving state-of-the-art log likelihood estimates. We investigate the use of AR models as density estimators in two settings -- as a lear…
TranslationTowards Scalable Persistence-Based Topological Optimization
Persistence-based topological optimization deforms a point cloud $X \subset \mathbb{R}^d$ by minimizing objectives of the form $L(X) = \ell(\mathrm{Dgm}(X))$, where $\mathrm{Dgm}(X)$ is a persistence diagram. In practice…
Topological Detection of Phenomenological Bifurcations with Unreliable Kernel Densities
Phenomenological (P-type) bifurcations are qualitative changes in stochastic dynamical systems whereby the stationary probability density function (PDF) changes its topology. The current state of the art for detecting th…
Topological Data AnalysisSinkhorn Divergence of Topological Signature Estimates for Time Series Classification
Distinguishing between classes of time series sampled from dynamic systems is a common challenge in systems and control engineering, for example in the context of health monitoring, fault detection, and quality control. …
ClassificationFault DetectionGeneral ClassificationTime Series+2Learning from Small Sample Sets by Combining Unsupervised Meta-Training with CNNs
This work explores CNNs for the recognition of novel categories from few examples. Inspired by the transferability properties of CNNs, we introduce an additional unsupervised meta-training stage that exposes multiple top…
Action RecognitionGeneral ClassificationScene ClassificationTemporal Action Localization