arXiv research

Improved Bayesian optimization for conditional parameter spaces.

In practical Bayesian optimization, we must often search over structures with differing numbers of parameters. For instance, we may wish to search over neural network architectures with an unknown number of layers. To relate performance data gathered for different architectures, we define a new kernel for conditional p…

Study stability of curvature-dimension condition for negative dimensions.

Develops theory for conditional optimal transport in infinite-dimensional spaces.

Indecomposable symmetric Lorentzian manifolds of non-constant curvature are called Cahen-Wallach spaces. Their isometry classes are described by continuous families of real parameters. We derive necessary and sufficient conditions for the existence of compact quotients of Cahen-Wallach spaces in terms of these paramete…

Conditions for uniquely identifying parameters of deep ReLU networks.

We study geodesics of the form $γ(t)=π(\exp(tX)\exp(tY))$, $X,Y\in \fr{g}=\operatorname{Lie}(G)$, in homogeneous spaces $G/K$, where $π:G\rightarrow G/K$ is the natural projection. These curves naturally generalise homogeneous geodesics, that is orbits of one-parameter subgroups of $G$ (i.e. $γ(t)=π(\exp (tX))$, $X\in …

The paper characterizes biconservative surfaces in hyperbolic 4-space.

Function-space MAP estimation leads to better generalization and robustness.

Sharp bounds on hyperbolic metrics in Ptolemaic spaces are derived.

Novel covariance function improves Bayesian optimization efficiency.

Training-free model learns SDE dynamics without training, accelerating parameter studies.

Gradient flow in parameters equals linear interpolation in outputs.

Machine learning pipeline potentially consists of several stages of operations like data preprocessing, feature engineering and machine learning model training. Each operation has a set of hyper-parameters, which can become irrelevant for the pipeline when the operation is not selected. This gives rise to a hierarchica…

The paper introduces canonical parameters for marginally trapped surfaces in Minkowski space.

IPMs struggle with hyperbolic spaces due to polynomially growing barrier parameters.

Generatability in metric spaces studied with novel novelty parameters.

Efficient estimators for smooth Hilbert-valued parameters with theoretical guarantees.

The article addresses a long-standing open problem on the justification of using variational Bayes methods for parameter estimation. We provide general conditions for obtaining optimal risk bounds for point estimates acquired from mean-field variational Bayesian inference. The conditions pertain to the existence of cer…

New method for estimating parameters in inverse problems using double robustness.

We consider the numerical stability of the parameter recovery problem in Linear Structural Equation Model ($\LSEM$) of causal inference. A long line of work starting from Wright (1920) has focused on understanding which sub-classes of $\LSEM$ allow for efficient parameter recovery. Despite decades of study, this questi…

Develops a new asymptotic efficiency theory for non-Euclidean parameter spaces.

In this work we give a method for constructing a one-parameter family of complete CMC-1 (i.e. constant mean curvature 1) surfaces in hyperbolic 3-space that correspond to a given complete minimal surface with finite total curvature in Euclidean 3-space. We show that this one-parameter family of surfaces with the same s…

We study the geometry of the tangent bundle equipped with a two-parameter family of Riemannian metrics. After deriving the expression of the Levi-Civita connection, we compute the Riemann curvature tensor and the sectional, Ricci and scalar curvatures. Specializing to the case of space forms, we characterise the metric…

Random complexes can be embedded linearly if certain conditions on parameters are met.

First we provide a simple set of sufficient conditions for the weak convergence of scaled affine processes with state space $R_+ \times R^d$. We specialize our result to one-dimensional continuous state branching processes with immigration. As an application, we study the asymptotic behavior of least squares estimators…

Quasi-alternating links are a generalization of alternating links. They are homologically thin for both Khovanov homology and knot Floer homology. Recent work of Greene and joint work of the first author with Kofman resulted in the classification of quasi-alternating pretzel links in terms of their integer tassel param…

There is a one-to-one correspondence between associated families of generic conformally flat (local-)hypersurfaces in 4-dimensional space forms and conformally flat 3-metrics with the Guichard condition. In this paper, we study the space of conformally flat 3-metrics with the Guichard condition: for a conformally flat …

New approach uses negative controls to estimate causal parameters without completeness conditions.

In many tasks, in particular in natural science, the goal is to determine hidden system parameters from a set of measurements. Often, the forward process from parameter- to measurement-space is a well-defined function, whereas the inverse problem is ambiguous: one measurement may map to multiple different sets of param…

Constructing compact non-Kähler manifolds with and without the Hard Lefschetz Condition

We consider a general regularised interpolation problem for learning a parameter vector from data. The well known representer theorem says that under certain conditions on the regulariser there exists a solution in the linear span of the data points. This is at the core of kernel methods in machine learning as it makes…

Incorporating domain knowledge into the modeling process is an effective way to improve learning accuracy. However, as it is provided by humans, domain knowledge can only be specified with some degree of uncertainty. We propose to explicitly model such uncertainty through probabilistic constraints over the parameter sp…

New PG samplers improve inference in coupled state-space models.

A new method debiases multiple target parameters without IFs.

Minimal surfaces of general type in Euclidean 4-space are characterized with the conditions that the ellipse of curvature at any point is centered at this point and has two different principal axes. Any minimal surface of general type locally admits geometrically determined parameters - canonical parameters. In such pa…

Proposes a new ARCH framework for Hilbert space data.

New learning rates for embeddings in RKHSs, even when the target is not Hilbert-Schmidt.

We obtain new sharp isoperimetric inequalities on a Riemannian manifold equipped with a probability measure, whose generalized Ricci curvature is bounded from below (possibly negatively), and generalized dimension and diameter of the convex support are bounded from above (possibly infinitely). Our inequalities are shar…

Minimal Kaehler submanifolds in low codimension are often minimal.

We investigate the dynamics of $2$-generator semigroups of polynomials with bounded planar postcritical set and associated random dynamics on the Riemann sphere. Also, we investigate the space ${\cal B}$ of such semigroups. We show that for a parameter $h$ in the intersection of ${\cal B}$, the hyperbolicity locus ${\c…

Investigates maps and properties in spaces with negative dimensions and curvature.

In this paper, we study the interaction between the geodesic orbit (g.o.~in short) property and certain flag curvature conditions. A Finsler manifold is called g.o.~if each constant speed geodesic is the orbit of a one-parameter subgroup. Besides the non-negatively curved condition, we also concern the (FP) condition f…

In this paper, we address the challenging problem of selecting tuning parameters for high-dimensional sparse regression. We propose a simple and computationally efficient method, called path thresholding (PaTh), that transforms any tuning parameter-dependent sparse regression algorithm into an asymptotically tuning-fre…

CoSMIC extends flow-based SVI to transdimensional problems.

We propose a novel framework for multi-task reinforcement learning (MTRL). Using a variational inference formulation, we learn policies that generalize across both changing dynamics and goals. The resulting policies are parametrized by shared parameters that allow for transfer between different dynamics and goal condit…

Generates consistent IV surfaces using VAEs and SDE models.

This study improves state estimation for nonlinear systems using conditional normalizing flows.