arXiv research

Study geometric structures on LVM threefolds, focusing on resonant structures.

A Python package solves source duplication in single channel LVMs using spectral regularisation.

Factorized information criterion (FIC) is a recently developed approximation technique for the marginal log-likelihood, which provides an automatic model selection framework for a few latent variable models (LVMs) with tractable inference algorithms. This paper reconsiders FIC and fills theoretical gaps of previous FIC…

This paper benchmarks speech LVMs against deterministic models and adapts a video model to speech.

New LVMs optimize any exponential family distribution without specific assumptions.

The Gaussian process latent variable model (GP-LVM) provides a flexible approach for non-linear dimensionality reduction that has been widely applied. However, the current approach for training GP-LVMs is based on maximum likelihood, where the latent projection variables are maximized over rather than integrated out. I…

LVM and LVMB manifolds are a large family of examples of non kähler manifolds. For instance, Hopf manifolds and Calabi-Eckmann manifolds can be seen as LVMB manifolds. The LVM manifolds have a very natural action of the real torus and the quotient of this action is a simple polytope. This quotient allows us to relate c…

LVM and LVMB manifolds are a large family of examples of non kahler manifolds. For instance, Hopf manifolds and Calabi-Eckmann manifolds can be seen as LVMB manifolds. The LVM manifolds have a very natural action of the real torus and the quotient of this action is a simple polytope. This quotient allows us to relate c…

Latent Variable Models (LVMs) are a large family of machine learning models providing a principled and effective way to extract underlying patterns, structure and knowledge from observed data. Due to the dramatic growth of volume and complexity of data, several new challenges have emerged and cannot be effectively addr…

We introduce the Locally Linear Latent Variable Model (LL-LVM), a probabilistic model for non-linear manifold discovery that describes a joint distribution over observations, their manifold coordinates and locally linear maps conditioned on a set of neighbourhood relationships. The model allows straightforward variatio…

To address three important issues involved in latent variable models (LVMs), including capturing infrequent patterns, achieving small-sized but expressive models and alleviating overfitting, several studies have been devoted to "diversifying" LVMs, which aim at encouraging the components in LVMs to be diverse. Most exi…

LIT-LVM improves linear predictors by estimating interaction terms with latent vectors.

This paper improves probabilistic latent models on hyperbolic spaces.

We present the Mixed Likelihood Gaussian process latent variable model (GP-LVM), capable of modeling data with attributes of different types. The standard formulation of GP-LVM assumes that each observation is drawn from a Gaussian distribution, which makes the model unsuited for data with e.g. categorical or nominal a…

LVM-GP solves PDEs with uncertainty using latent variables and Gaussian processes.

The paper classifies diffeomorphism classes of Calabi-Yau threefolds constructed by gluing methods.

Estimating covariances between financial assets plays an important role in risk management. In practice, when the sample size is small compared to the number of variables, the empirical estimate is known to be very unstable. Here, we propose a novel covariance estimator based on the Gaussian Process Latent Variable Mod…

Optimizes bounds for threefold singularity volumes.

Study classifies Calabi-Yau threefolds with non-Gorenstein involutions.

spex-LVM infers interpretable latent factors from biomedical data.

The study classifies holomorphic projective connections on complex threefolds.

The Gaussian Process Latent Variable Model (GP-LVM) is a non-linear probabilistic method of embedding a high dimensional dataset in terms low dimensional `latent' variables. In this paper we illustrate that maximum a posteriori (MAP) estimation of the latent variables and hyperparameters can be used for model selection…

K-stability proven for a specific type of Fano threefold.

We study the variety of Poisson structures and compute Poisson cohomology for two families of Fano threefolds - smooth cubic threefolds and the del Pezzo quintic threefold. Along the way we reobtain by a different method earlier results of Loray, Pereira and Touzet in the special case we are considering.

Study noncommutative deformations of Calabi-Yau threefolds.

The study examines non-Kähler threefolds with specific metrics and finds they are quasi-bundles over surfaces.

New research confirms Kähler-Einstein metrics for all Fano threefolds of degree 22.

The authors give a complete classification of projective threefolds admitting a holomorphic conformal structure. A Corollary is the complete list of projective threefolds, whose tangent bundle is a symmetric square.

We consider a version of Hermitian-Einstein equation but perturbed by a Higgs field with a solution called a Donaldson-Thomas instanton on compact Kähler threefolds. The equation could be thought of as a generalization of the Hitchin equation on Riemann surfaces to Kähler threefolds. In the appendix of arXiv:0805.2192,…

We consider the connected-sum method of constructing compact Riemannian 7-manifolds with holonomy G_2 developed in math.DG/0012189. The method requires pairs of projective complex threefolds endowed with anticanonical K3 divisors, the latter `matching' via a certain non-holomorphic map. Suitable examples of threefolds …

Study on balanced Hermitian threefolds with parallel Bismut torsion.

Lecture notes on non-Kähler complex threefolds, focusing on conifold transitions.

We investigate geometric invariants of the one parameter family of Mukai threefolds that admit $\mathbb C^{*}$ action. In particular we find the invariant divisors in the anticanonical system, and thus establish a bound on the log canonical thresholds. Furthermore we find an explicit description of such threefolds in t…

Kähler-Ricci flow shows type II singularity on Fano threefolds.

It is challenging to develop stochastic gradient based scalable inference for deep discrete latent variable models (LVMs), due to the difficulties in not only computing the gradients, but also adapting the step sizes to different latent factors and hidden layers. For the Poisson gamma belief network (PGBN), a recently …

Study shows Futaki invariant vanishes on most Fano threefolds.

Found a stable 3D shape with specific properties.

We study local, global and local-to-global properties of threefolds with certain singularities. We prove criteria for these threefolds to be rational homology manifolds and conditions for threefolds to satisfy rational Poincaré duality. We relate the topological Euler characteristic of elliptic Calabi-Yau threefolds wi…

Complex manifolds can only map to curves, restricting Clemens threefolds and $S^6$.

We show that a smooth complex projective threefold admits a holomorphic one-form without zeros if and only if the underlying real 6-manifold fibres smoothly over the circle, and we give a complete classification of all threefolds with that property. Our results prove a conjecture of Kotschick in dimension three.

We study the problem of existence of Kähler--Einstein metrics on smooth Fano threefolds of Picard rank one and anticanonical degree $22$ that admit a faithful action of the multiplicative group $\mathbb{C}^\ast$. We prove that, except possibly two explicitly described cases, all such smooth Fano threefolds are Kähler--…

The study classifies Kähler threefolds with special fiber bundles.

We present a probabilistic model for unsupervised alignment of high-dimensional time-warped sequences based on the Dirichlet Process Mixture Model (DPMM). We follow the approach introduced in (Kazlauskaite, 2018) of simultaneously representing each data sequence as a composition of a true underlying function and a time…

We prove a case of the conjecture of Douglas, Reinbacher and Yau about the existence of stable vector bundles with prescribed Chern classes on a Calabi-Yau threefold. For this purpose we prove the existence of certain stable vector bundle extensions over elliptically fibered Calabi-Yau threefolds.

We study real lines on certain Moishezon threefolds which are potentially twistor spaces of 3CP^2. Here, line means a smooth rational curve whose normal bundle is O(1)^2 and the reality implies the invariance under an anti-holomorphic involution on the threefolds. Our threefolds are birational to double coverings of CP…

We construct balanced metrics on the family of non-Kähler Calabi-Yau threefolds that are obtained by smoothing after contracting $(-1,-1)$-rational curves on Kähler Calabi-Yau threefold. As an application, we construct balanced metrics on complex manifolds diffeomorphic to connected sum of $k\geq 2$ copies of $S^3\time…

The Gaussian process latent variable model (GP-LVM) is a popular approach to non-linear probabilistic dimensionality reduction. One design choice for the model is the number of latent variables. We present a spike and slab prior for the GP-LVM and propose an efficient variational inference procedure that gives a lower …

Algorithm computes eigenvalues and eigenforms on Calabi-Yau threefolds.