相关论文: Invariant Bayesian estimation on manifolds

We define a number of natural (from geometric and combinatorial points of view) deformation spaces of valuations on finite graphs, and study functions over these deformation spaces. These functions include both direct metric invariants…

Deep generative priors offer powerful models for complex-structured data, such as images, audio, and text. Using these priors in inverse problems typically requires estimating the input and/or hidden signals in a multi-layer deep neural…

We consider the nonparametric multivariate isotonic regression problem, where the regression function is assumed to be nondecreasing with respect to each predictor. Our goal is to construct a Bayesian credible interval for the function…

Some model reduction techniques for multiple time-scale dynamical systems make use of the identification of low dimensional slow invariant attracting manifolds (SIAM) in order to reduce the dimensionality of the phase space by restriction…

The maximum a-posteriori (MAP) perturbation framework has emerged as a useful approach for inference and learning in high dimensional complex models. By maximizing a randomly perturbed potential function, MAP perturbations generate unbiased…

As modern neural networks get more complex, specifying a model with high predictive performance and sound uncertainty quantification becomes a more challenging task. Despite some promising theoretical results on the true posterior…

Transformation-invariant analysis of signals often requires the computation of the distance from a test pattern to a transformation manifold. In particular, the estimation of the distances between a transformed query signal and several…

Alignment between non-rigid stretchable structures is one of the most challenging tasks in computer vision, as the invariant properties are hard to define, and there is no labeled data for real datasets. We present unsupervised neural…

Generalized approximate message passing (GAMP) is a promising technique for unknown signal reconstruction of generalized linear models (GLM). However, it requires that the transformation matrix has independent and identically distributed…

We introduce the price of symmetrisation, a concept that aims to compare fundamental differences (gap and quotient) between values of a given graph invariant for digraphs and the values of the same invariant of the symmetric versions of…

Deep neural networks have achieved great success in the last decade. When designing neural networks to handle the ubiquitous geometric data such as point clouds and graphs, it is critical that the model can maintain invariance towards…

In computational inverse problems, it is common that a detailed and accurate forward model is approximated by a computationally less challenging substitute. The model reduction may be necessary to meet constraints in computing time when…

This paper proposes two distinct contributions to econometric analysis of large information sets and structural instabilities. First, it treats a regression model with time-varying coefficients, stochastic volatility and exogenous…

Manifold-valued parameters routinely arise in modern statistical applications such as in medical imaging, robotics, and computer vision, to name a few. While traditional Bayesian approaches are applicable to such settings by considering an…

Distribution regression has recently attracted much interest as a generic solution to the problem of supervised learning where labels are available at the group level, rather than at the individual level. Current approaches, however, do not…

We studied topological and metric properties of the so-called interval translation maps (ITMs). For these maps, we introduced the maximal invariant measure and study its properties. Further, we study how the invariant measures depend on the…

Vector approximate message passing (VAMP) is an efficient approximate inference algorithm used for generalized linear models. Although VAMP exhibits excellent performance, particularly when measurement matrices are sampled from rotationally…

Integrated sensing and communication is regarded as a key enabler for next-generation wireless networks. To optimize the transmitted waveform for both sensing and communication, various performance metrics must be considered. This work…

Minimum numbers decide e.g. whether a given map f: S^m --> S^n/G from a sphere into a spherical space form can be deformed to a map f' such that f(x) not equal f'(x) for all x in S^m. In this paper we compare minimum numbers to…

Bayesian Neural Networks provide a principled framework for uncertainty quantification by modeling the posterior distribution of network parameters. However, exact posterior inference is computationally intractable, and widely used…