Search Results for author: Simo Särkkä

Found 49 papers, 23 papers with code

Conditioning diffusion models by explicit forward-backward bridging

1 code implementation22 May 2024 Adrien Corenflos, Zheng Zhao, Simo Särkkä, Jens Sjölund, Thomas B. Schön

Given an unconditional diffusion model $\pi(x, y)$, using it to perform conditional simulation $\pi(x \mid y)$ is still largely an open question and is typically achieved by learning conditional drifts to the denoising SDE after the fact.

Denoising

Utilizing U-Net Architectures with Auxiliary Information for Scatter Correction in CBCT Across Different Field-of-View Settings

no code implementations27 Feb 2024 Harshit Agrawal, Ari Hietanen, Simo Särkkä

Our findings suggest that this novel approach outperforms the baseline U-Net, offering a significant step towards practical application in real clinical settings where CBCT systems are employed to scan a wide range of FOVs.

Nesting Particle Filters for Experimental Design in Dynamical Systems

1 code implementation12 Feb 2024 Sahel Iqbal, Adrien Corenflos, Simo Särkkä, Hany Abdulsamad

In this paper, we propose a novel approach to Bayesian experimental design for non-exchangeable data that formulates it as risk-sensitive policy optimization.

Experimental Design

Quantum-Assisted Hilbert-Space Gaussian Process Regression

1 code implementation1 Feb 2024 Ahmad Farooq, Cristian A. Galvis-Florez, Simo Särkkä

Gaussian processes are probabilistic models that are commonly used as functional priors in machine learning.

Gaussian Processes regression

Risk-Sensitive Stochastic Optimal Control as Rao-Blackwellized Markovian Score Climbing

1 code implementation21 Dec 2023 Hany Abdulsamad, Sahel Iqbal, Adrien Corenflos, Simo Särkkä

Stochastic optimal control of dynamical systems is a crucial challenge in sequential decision-making.

Decision Making

Nonparametric modeling of the composite effect of multiple nutrients on blood glucose dynamics

1 code implementation6 Nov 2023 Arina Odnoblyudova, Çağlar Hızlı, ST John, Andrea Cognolato, Anne Juuti, Simo Särkkä, Kirsi Pietiläinen, Pekka Marttinen

By differentiating treatment components, incorporating their dosages, and sharing statistical information across patients via a hierarchical multi-output Gaussian process, our method improves prediction accuracy over existing approaches, and allows us to interpret the different effects of carbohydrates and fat on the overall glucose response.

Parallel-in-Time Probabilistic Numerical ODE Solvers

1 code implementation2 Oct 2023 Nathanael Bosch, Adrien Corenflos, Fatemeh Yaghoobi, Filip Tronarp, Philipp Hennig, Simo Särkkä

Probabilistic numerical solvers for ordinary differential equations (ODEs) treat the numerical simulation of dynamical systems as problems of Bayesian state estimation.

A Recursive Newton Method for Smoothing in Nonlinear State Space Models

no code implementations15 Jun 2023 Fatemeh Yaghoobi, Hany Abdulsamad, Simo Särkkä

In this paper, we use the optimization formulation of nonlinear Kalman filtering and smoothing problems to develop second-order variants of iterated Kalman smoother (IKS) methods.

Auxiliary MCMC and particle Gibbs samplers for parallelisable inference in latent dynamical systems

1 code implementation1 Mar 2023 Adrien Corenflos, Simo Särkkä

We introduce two new classes of exact Markov chain Monte Carlo (MCMC) samplers for inference in latent dynamical models.

Deep learning based projection domain metal segmentation for metal artifact reduction in cone beam computed tomography

no code implementations17 Aug 2022 Harshit Agrawal, Ari Hietanen, Simo Särkkä

We compare our model's performance on real clinical scans with conventional region growing threshold-based MAR, moving metal artifact reduction method, and a recent deep learning method.

Anatomy Metal Artifact Reduction +1

Online Pole Segmentation on Range Images for Long-term LiDAR Localization in Urban Environments

1 code implementation15 Aug 2022 Hao Dong, Xieyuanli Chen, Simo Särkkä, Cyrill Stachniss

We further use the extracted poles as pseudo labels to train a deep neural network for online range image-based pole segmentation.

Probabilistic Estimation of Instantaneous Frequencies of Chirp Signals

1 code implementation12 May 2022 Zheng Zhao, Simo Särkkä, Jens Sjölund, Thomas B. Schön

We present a continuous-time probabilistic approach for estimating the chirp signal and its instantaneous frequency function when the true forms of these functions are not accessible.

Gaussian Processes

De-Sequentialized Monte Carlo: a parallel-in-time particle smoother

1 code implementation4 Feb 2022 Adrien Corenflos, Nicolas Chopin, Simo Särkkä

We propose dSMC (de-Sequentialized Monte Carlo), a new particle smoother that is able to process $T$ observations in $\mathcal{O}(\log T)$ time on parallel architecture.

Bayes-Newton Methods for Approximate Bayesian Inference with PSD Guarantees

1 code implementation2 Nov 2021 William J. Wilkinson, Simo Särkkä, Arno Solin

We formulate natural gradient variational inference (VI), expectation propagation (EP), and posterior linearisation (PL) as extensions of Newton's method for optimising the parameters of a Bayesian posterior distribution.

Bayesian Inference Gaussian Processes +2

Hierarchical Non-Stationary Temporal Gaussian Processes With $L^1$-Regularization

no code implementations20 May 2021 Zheng Zhao, Rui Gao, Simo Särkkä

This paper is concerned with regularized extensions of hierarchical non-stationary temporal Gaussian processes (NSGPs) in which the parameters (e. g., length-scale) are modeled as GPs.

Gaussian Processes regression

Temporal Gaussian Process Regression in Logarithmic Time

1 code implementation19 Feb 2021 Adrien Corenflos, Zheng Zhao, Simo Särkkä

The aim of this article is to present a novel parallelization method for temporal Gaussian process (GP) regression problems.

regression

Temporal Parallelization of Inference in Hidden Markov Models

1 code implementation10 Feb 2021 Sakira Hassan, Simo Särkkä, Ángel F. García-Fernández

This paper presents algorithms for parallelization of inference in hidden Markov models (HMMs).

A probabilistic Taylor expansion with Gaussian processes

no code implementations1 Feb 2021 Toni Karvonen, Jon Cockayne, Filip Tronarp, Simo Särkkä

We study a class of Gaussian processes for which the posterior mean, for a particular choice of data, replicates a truncated Taylor expansion of any order.

Gaussian Processes regression

Deep State-Space Gaussian Processes

1 code implementation11 Aug 2020 Zheng Zhao, Muhammad Emzir, Simo Särkkä

This paper is concerned with a state-space approach to deep Gaussian process (DGP) regression.

Gaussian Processes regression

Non-Stationary Multi-layered Gaussian Priors for Bayesian Inversion

1 code implementation28 Jun 2020 Muhammad Emzir, Sari Lasanen, Zenith Purisha, Lassi Roininen, Simo Särkkä

In this article, we study Bayesian inverse problems with multi-layered Gaussian priors.

Statistics Theory Statistics Theory

Continuous-Discrete Filtering and Smoothing on Submanifolds of Euclidean Space

no code implementations17 Apr 2020 Filip Tronarp, Simo Särkkä

For approximate filtering and smoothing the projection approach is taken, where it turns out that the prediction and smoothing equations are the same as in the case when the state variable evolves in Euclidean space.

Maximum likelihood estimation and uncertainty quantification for Gaussian process approximation of deterministic functions

no code implementations29 Jan 2020 Toni Karvonen, George Wynne, Filip Tronarp, Chris. J. Oates, Simo Särkkä

We show that the maximum likelihood estimation of the scale parameter alone provides significant adaptation against misspecification of the Gaussian process model in the sense that the model can become "slowly" overconfident at worst, regardless of the difference between the smoothness of the data-generating function and that expected by the model.

regression Uncertainty Quantification

Taylor Moment Expansion for Continuous-Discrete Gaussian Filtering and Smoothing

2 code implementations8 Jan 2020 Zheng Zhao, Toni Karvonen, Roland Hostettler, Simo Särkkä

The paper is concerned with non-linear Gaussian filtering and smoothing in continuous-discrete state-space models, where the dynamic model is formulated as an It\^{o} stochastic differential equation (SDE), and the measurements are obtained at discrete time instants.

The Use of Gaussian Processes in System Identification

no code implementations13 Jul 2019 Simo Särkkä

Gaussian process state-space models (GPSS) can be used to learn the dynamic and measurement models for a state-space representation of the input-output data.

Gaussian Processes Time Series +1

Kalman-based Spectro-Temporal ECG Analysis using Deep Convolutional Networks for Atrial Fibrillation Detection

no code implementations12 Dec 2018 Zheng Zhao, Simo Särkkä, Ali Bahrami Rad

In this article, we propose a novel ECG classification framework for atrial fibrillation (AF) detection using spectro-temporal representation (i. e., time varying spectrum) and deep convolutional networks.

Atrial Fibrillation Detection ECG Classification

Improved Calibration of Numerical Integration Error in Sigma-Point Filters

no code implementations28 Nov 2018 Jakub Prüher, Toni Karvonen, Chris. J. Oates, Ondřej Straka, Simo Särkkä

The sigma-point filters, such as the UKF, which exploit numerical quadrature to obtain an additional order of accuracy in the moment transformation step, are popular alternatives to the ubiquitous EKF.

Numerical Integration Uncertainty Quantification

LSD$_2$ -- Joint Denoising and Deblurring of Short and Long Exposure Images with CNNs

no code implementations23 Nov 2018 Janne Mustaniemi, Juho Kannala, Jiri Matas, Simo Särkkä, Janne Heikkilä

The paper addresses the problem of acquiring high-quality photographs with handheld smartphone cameras in low-light imaging conditions.

Deblurring Denoising

Probabilistic Solutions To Ordinary Differential Equations As Non-Linear Bayesian Filtering: A New Perspective

1 code implementation8 Oct 2018 Filip Tronarp, Hans Kersting, Simo Särkkä, Philipp Hennig

We formulate probabilistic numerical approximations to solutions of ordinary differential equations (ODEs) as problems in Gaussian process (GP) regression with non-linear measurement functions.

Gyroscope-Aided Motion Deblurring with Deep Networks

1 code implementation1 Oct 2018 Janne Mustaniemi, Juho Kannala, Simo Särkkä, Jiri Matas, Janne Heikkilä

We propose a deblurring method that incorporates gyroscope measurements into a convolutional neural network (CNN).

Deblurring

Symmetry Exploits for Bayesian Cubature Methods

1 code implementation26 Sep 2018 Toni Karvonen, Simo Särkkä, Chris. J. Oates

Bayesian cubature provides a flexible framework for numerical integration, in which a priori knowledge on the integrand can be encoded and exploited.

Methodology Numerical Analysis Computation

Gaussian process classification using posterior linearisation

no code implementations13 Sep 2018 Ángel F. García-Fernández, Filip Tronarp, Simo Särkkä

This paper proposes a new algorithm for Gaussian process classification based on posterior linearisation (PL).

Classification General Classification

Probabilistic approach to limited-data computed tomography reconstruction

no code implementations11 Sep 2018 Zenith Purisha, Carl Jidling, Niklas Wahlström, Simo Särkkä, Thomas B. Schön

The approach also allows for reformulation of come classical regularization methods as Laplacian and Tikhonov regularization as Gaussian process regression, and hence provides an efficient algorithm and principled means for their parameter tuning.

Numerical Integration

Fast Motion Deblurring for Feature Detection and Matching Using Inertial Measurements

no code implementations22 May 2018 Janne Mustaniemi, Juho Kannala, Simo Särkkä, Jiri Matas, Janne Heikkilä

It is well-known that motion blur decreases the performance of traditional feature detectors and descriptors.

Deblurring

Gaussian Process Latent Force Models for Learning and Stochastic Control of Physical Systems

no code implementations15 Sep 2017 Simo Särkkä, Mauricio A. Álvarez, Neil D. Lawrence

This article is concerned with learning and stochastic control in physical systems which contain unknown input signals.

Gaussian Processes

Student-t Process Quadratures for Filtering of Non-Linear Systems with Heavy-Tailed Noise

no code implementations15 Mar 2017 Jakub Prüher, Filip Tronarp, Toni Karvonen, Simo Särkkä, Ondřej Straka

Advantage of the Student- t process quadrature over the traditional Gaussian process quadrature, is that the integral variance depends also on the function values, allowing for a more robust modelling of the integration error.

Inertial-Based Scale Estimation for Structure from Motion on Mobile Devices

1 code implementation29 Nov 2016 Janne Mustaniemi, Juho Kannala, Simo Särkkä, Jiri Matas, Janne Heikkilä

In the process, we also perform a temporal and spatial alignment of the camera and the IMU.

Parallelizable sparse inverse formulation Gaussian processes (SpInGP)

no code implementations25 Oct 2016 Alexander Grigorievskiy, Neil Lawrence, Simo Särkkä

We propose a parallelizable sparse inverse formulation Gaussian process (SpInGP) for temporal models.

Gaussian Processes

A probabilistic model for the numerical solution of initial value problems

1 code implementation17 Oct 2016 Michael Schober, Simo Särkkä, Philipp Hennig

Like many numerical methods, solvers for initial value problems (IVPs) on ordinary differential equations estimate an analytically intractable quantity, using the results of tractable computations as inputs.

Regularizing Solutions to the MEG Inverse Problem Using Space-Time Separable Covariance Functions

no code implementations17 Apr 2016 Arno Solin, Pasi Jylänki, Jaakko Kauramäki, Tom Heskes, Marcel A. J. van Gerven, Simo Särkkä

We apply the method to both simulated and empirical data, and demonstrate the efficiency and generality of our Bayesian source reconstruction approach which subsumes various classical approaches in the literature.

Computationally Efficient Bayesian Learning of Gaussian Process State Space Models

no code implementations7 Jun 2015 Andreas Svensson, Arno Solin, Simo Särkkä, Thomas B. Schön

We present a procedure for efficient Bayesian learning in Gaussian process state space models, where the representation is formed by projecting the problem onto a set of approximate eigenfunctions derived from the prior covariance structure.

Gaussian Processes

Sigma-Point Filtering and Smoothing Based Parameter Estimation in Nonlinear Dynamic Systems

1 code implementation23 Apr 2015 Juho Kokkala, Arno Solin, Simo Särkkä

We consider approximate maximum likelihood parameter estimation in nonlinear state-space models.

Methodology Dynamical Systems Optimization and Control Computation

On the relation between Gaussian process quadratures and sigma-point methods

no code implementations22 Apr 2015 Simo Särkkä, Jouni Hartikainen, Lennart Svensson, Fredrik Sandblom

This article is concerned with Gaussian process quadratures, which are numerical integration methods based on Gaussian process regression methods, and sigma-point methods, which are used in advanced non-linear Kalman filtering and smoothing algorithms.

Numerical Integration regression +1

Hilbert Space Methods for Reduced-Rank Gaussian Process Regression

2 code implementations21 Jan 2014 Arno Solin, Simo Särkkä

On this approximate eigenbasis the eigenvalues of the covariance function can be expressed as simple functions of the spectral density of the Gaussian process, which allows the GP inference to be solved under a computational cost scaling as $\mathcal{O}(nm^2)$ (initial) and $\mathcal{O}(m^3)$ (hyperparameter learning) with $m$ basis functions and $n$ data points.

regression

The Coloured Noise Expansion and Parameter Estimation of Diffusion Processes

no code implementations NeurIPS 2012 Simon Lyons, Amos J. Storkey, Simo Särkkä

The decomposition allows us to take a diffusion process of interest and cast it in a form that is amenable to sampling by MCMC methods.

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