arXiv subjects

Fredrik Lindsten

Publications and source records attributed to Fredrik Lindsten.

At least 37 records · Page 2Linked to original sources

arXiv2025

Building Machine Learning Limited Area Models: Kilometer-Scale Weather Forecasting in Realistic Settings

Machine learning is revolutionizing global weather forecasting, with models that efficiently produce highly accurate forecasts. Apart from global forecasting there is also a large value in high-resolution regional weather forecasts, focusing on accurate simulations of the atmosphere for a limited area. Initial attempts have been made to use machine learning for such limited area scenarios, but these experiments do not consider realistic forecasting settings and do not investigate the many design choices involved. We present a framework for building kilometer-scale machine learning limited area models with boundary conditions imposed through a flexible boundary forcing method. This enables boundary conditions defined either from reanalysis or operational forecast data. Our approach employs specialized graph constructions with rectangular and triangular meshes, along with multi-step rollout training strategies to improve temporal consistency. We perform systematic evaluation of different design choices, including the boundary width, graph construction and boundary forcing integration. Models are evaluated across both a Danish and a Swiss domain, two regions that exhibit different orographical characteristics. Verification is performed against both gridded analysis data and in-situ observations, including a case study for the storm Ciara in February 2020. Both models achieve skillful predictions across a wide range of variables, with our Swiss model outperforming the numerical weather prediction baseline for key surface variables. With their substantially lower computational cost, our findings demonstrate great potential for machine learning limited area models in the future of regional weather forecasting.

physics.ao-ph↗

arXiv2025

Diffusion-LAM: Probabilistic Limited Area Weather Forecasting with Diffusion

Machine learning methods have been shown to be effective for weather forecasting, based on the speed and accuracy compared to traditional numerical models. While early efforts primarily concentrated on deterministic predictions, the field has increasingly shifted toward probabilistic forecasting to better capture the forecast uncertainty. Most machine learning-based models have been designed for global-scale predictions, with only limited work targeting regional or limited area forecasting, which allows more specialized and flexible modeling for specific locations. This work introduces Diffusion-LAM, a probabilistic limited area weather model leveraging conditional diffusion. By conditioning on boundary data from surrounding regions, our approach generates forecasts within a defined area. Experimental results on the MEPS limited area dataset demonstrate the potential of Diffusion-LAM to deliver accurate probabilistic forecasts, highlighting its promise for limited-area weather prediction.

cs.LG↗

arXiv2025

cryoSPHERE: Single-particle heterogeneous reconstruction from cryo EM

The three-dimensional structure of proteins plays a crucial role in determining their function. Protein structure prediction methods, like AlphaFold, offer rapid access to a protein structure. However, large protein complexes cannot be reliably predicted, and proteins are dynamic, making it important to resolve their full conformational distribution. Single-particle cryo-electron microscopy (cryo-EM) is a powerful tool for determining the structures of large protein complexes. Importantly, the numerous images of a given protein contain underutilized information about conformational heterogeneity. These images are very noisy projections of the protein, and traditional methods for cryo-EM reconstruction are limited to recovering only one or a few consensus conformations. In this paper, we introduce cryoSPHERE, which is a deep learning method that uses a nominal protein structure (e.g., from AlphaFold) as input, learns how to divide it into segments, and moves these segments as approximately rigid bodies to fit the different conformations present in the cryo-EM dataset. This approach provides enough constraints to enable meaningful reconstructions of single protein structural ensembles. We demonstrate this with two synthetic datasets featuring varying levels of noise, as well as two real dataset. We show that cryoSPHERE is very resilient to the high levels of noise typically encountered in experiments, where we see consistent improvements over the current state-of-the-art for heterogeneous reconstruction.

q-bio.BM↗

arXiv2024

Elements of Sequential Monte Carlo

A core problem in statistics and probabilistic machine learning is to compute probability distributions and expectations. This is the fundamental problem of Bayesian statistics and machine learning, which frames all inference as expectations with respect to the posterior distribution. The key challenge is to approximate these intractable expectations. In this tutorial, we review sequential Monte Carlo (SMC), a random-sampling-based class of methods for approximate inference. First, we explain the basics of SMC, discuss practical issues, and review theoretical results. We then examine two of the main user design choices: the proposal distributions and the so called intermediate target distributions. We review recent results on how variational inference and amortization can be used to learn efficient proposals and target distributions. Next, we discuss the SMC estimate of the normalizing constant, how this can be used for pseudo-marginal inference and inference evaluation. Throughout the tutorial we illustrate the use of SMC on various models commonly used in machine learning, such as stochastic recurrent neural networks, probabilistic graphical models, and probabilistic programs.

stat.ML↗

arXiv2024

Probabilistic Weather Forecasting with Hierarchical Graph Neural Networks

In recent years, machine learning has established itself as a powerful tool for high-resolution weather forecasting. While most current machine learning models focus on deterministic forecasts, accurately capturing the uncertainty in the chaotic weather system calls for probabilistic modeling. We propose a probabilistic weather forecasting model called Graph-EFM, combining a flexible latent-variable formulation with the successful graph-based forecasting framework. The use of a hierarchical graph construction allows for efficient sampling of spatially coherent forecasts. Requiring only a single forward pass per time step, Graph-EFM allows for fast generation of arbitrarily large ensembles. We experiment with the model on both global and limited area forecasting. Ensemble forecasts from Graph-EFM achieve equivalent or lower errors than comparable deterministic models, with the added benefit of accurately capturing forecast uncertainty.

cs.LG↗

arXiv2024

On Partial Prototype Collapse in the DINO Family of Self-Supervised Methods

A prominent self-supervised learning paradigm is to model the representations as clusters, or more generally as a mixture model. Learning to map the data samples to compact representations and fitting the mixture model simultaneously leads to the representation collapse problem. Regularizing the distribution of data points over the clusters is the prevalent strategy to avoid this issue. While this is sufficient to prevent full representation collapse, we show that a partial prototype collapse problem still exists in the DINO family of methods, that leads to significant redundancies in the prototypes. Such prototype redundancies serve as shortcuts for the method to achieve a marginal latent class distribution that matches the prescribed prior. We show that by encouraging the model to use diverse prototypes, the partial prototype collapse can be mitigated. Effective utilization of the prototypes enables the methods to learn more fine-grained clusters, encouraging more informative representations. We demonstrate that this is especially beneficial when pre-training on a long-tailed fine-grained dataset.

cs.LG↗

arXiv2024

Discriminator Guidance for Autoregressive Diffusion Models

We introduce discriminator guidance in the setting of Autoregressive Diffusion Models. The use of a discriminator to guide a diffusion process has previously been used for continuous diffusion models, and in this work we derive ways of using a discriminator together with a pretrained generative model in the discrete case. First, we show that using an optimal discriminator will correct the pretrained model and enable exact sampling from the underlying data distribution. Second, to account for the realistic scenario of using a sub-optimal discriminator, we derive a sequential Monte Carlo algorithm which iteratively takes the predictions from the discriminator into account during the generation process. We test these approaches on the task of generating molecular graphs and show how the discriminator improves the generative performance over using only the pretrained model.

cs.LG↗

arXiv2024

Towards Understanding Epoch-wise Double descent in Two-layer Linear Neural Networks

Epoch-wise double descent is the phenomenon where generalisation performance improves beyond the point of overfitting, resulting in a generalisation curve exhibiting two descents under the course of learning. Understanding the mechanisms driving this behaviour is crucial not only for understanding the generalisation behaviour of machine learning models in general, but also for employing conventional selection methods, such as the use of early stopping to mitigate overfitting. While we ultimately want to draw conclusions of more complex models, such as deep neural networks, a majority of theoretical results regarding the underlying cause of epoch-wise double descent are based on simple models, such as standard linear regression. In this paper, to take a step towards more complex models in theoretical analysis, we study epoch-wise double descent in two-layer linear neural networks. First, we derive a gradient flow for the linear two-layer model, that bridges the learning dynamics of the standard linear regression model, and the linear two-layer diagonal network with quadratic weights. Second, we identify additional factors of epoch-wise double descent emerging with the extra model layer, by deriving necessary conditions for the generalisation error to follow a double descent pattern. While epoch-wise double descent in linear regression has been attributed to differences in input variance, in the two-layer model, also the singular values of the input-output covariance matrix play an important role. This opens up for further questions regarding unidentified factors of epoch-wise double descent for truly deep models.

stat.ML↗

arXiv2024

Active Learning with Weak Supervision for Gaussian Processes

Annotating data for supervised learning can be costly. When the annotation budget is limited, active learning can be used to select and annotate those observations that are likely to give the most gain in model performance. We propose an active learning algorithm that, in addition to selecting which observation to annotate, selects the precision of the annotation that is acquired. Assuming that annotations with low precision are cheaper to obtain, this allows the model to explore a larger part of the input space, with the same annotation budget. We build our acquisition function on the previously proposed BALD objective for Gaussian Processes, and empirically demonstrate the gains of being able to adjust the annotation precision in the active learning loop.

stat.ML↗

arXiv2024

DINO as a von Mises-Fisher mixture model

Self-distillation methods using Siamese networks are popular for self-supervised pre-training. DINO is one such method based on a cross-entropy loss between $K$-dimensional probability vectors, obtained by applying a softmax function to the dot product between representations and learnt prototypes. Given the fact that the learned representations are $L^2$-normalized, we show that DINO and its derivatives, such as iBOT, can be interpreted as a mixture model of von Mises-Fisher components. With this interpretation, DINO assumes equal precision for all components when the prototypes are also $L^2$-normalized. Using this insight we propose DINO-vMF, that adds appropriate normalization constants when computing the cluster assignment probabilities. Unlike DINO, DINO-vMF is stable also for the larger ViT-Base model with unnormalized prototypes. We show that the added flexibility of the mixture model is beneficial in terms of better image representations. The DINO-vMF pre-trained model consistently performs better than DINO on a range of downstream tasks. We obtain similar improvements for iBOT-vMF vs iBOT and thereby show the relevance of our proposed modification also for other methods derived from DINO.

cs.LG↗

arXiv2024

On the connection between Noise-Contrastive Estimation and Contrastive Divergence

Noise-contrastive estimation (NCE) is a popular method for estimating unnormalised probabilistic models, such as energy-based models, which are effective for modelling complex data distributions. Unlike classical maximum likelihood (ML) estimation that relies on importance sampling (resulting in ML-IS) or MCMC (resulting in contrastive divergence, CD), NCE uses a proxy criterion to avoid the need for evaluating an often intractable normalisation constant. Despite apparent conceptual differences, we show that two NCE criteria, ranking NCE (RNCE) and conditional NCE (CNCE), can be viewed as ML estimation methods. Specifically, RNCE is equivalent to ML estimation combined with conditional importance sampling, and both RNCE and CNCE are special cases of CD. These findings bridge the gap between the two method classes and allow us to apply techniques from the ML-IS and CD literature to NCE, offering several advantageous extensions.

stat.ML↗

arXiv2023

Graph-based Neural Weather Prediction for Limited Area Modeling

The rise of accurate machine learning methods for weather forecasting is creating radical new possibilities for modeling the atmosphere. In the time of climate change, having access to high-resolution forecasts from models like these is also becoming increasingly vital. While most existing Neural Weather Prediction (NeurWP) methods focus on global forecasting, an important question is how these techniques can be applied to limited area modeling. In this work we adapt the graph-based NeurWP approach to the limited area setting and propose a multi-scale hierarchical model extension. Our approach is validated by experiments with a local model for the Nordic region.

cs.LG↗

arXiv2023

Temporal Graph Neural Networks for Irregular Data

This paper proposes a temporal graph neural network model for forecasting of graph-structured irregularly observed time series. Our TGNN4I model is designed to handle both irregular time steps and partial observations of the graph. This is achieved by introducing a time-continuous latent state in each node, following a linear Ordinary Differential Equation (ODE) defined by the output of a Gated Recurrent Unit (GRU). The ODE has an explicit solution as a combination of exponential decay and periodic dynamics. Observations in the graph neighborhood are taken into account by integrating graph neural network layers in both the GRU state update and predictive model. The time-continuous dynamics additionally enable the model to make predictions at arbitrary time steps. We propose a loss function that leverages this and allows for training the model for forecasting over different time horizons. Experiments on simulated data and real-world data from traffic and climate modeling validate the usefulness of both the graph structure and time-continuous dynamics in settings with irregular observations.

stat.ML↗

arXiv2022

Nonlinear System Identification: Learning while respecting physical models using a sequential Monte Carlo method

Identification of nonlinear systems is a challenging problem. Physical knowledge of the system can be used in the identification process to significantly improve the predictive performance by restricting the space of possible mappings from the input to the output. Typically, the physical models contain unknown parameters that must be learned from data. Classical methods often restrict the possible models or have to resort to approximations of the model that introduce biases. Sequential Monte Carlo methods enable learning without introducing any bias for a more general class of models. In addition, they can also be used to approximate a posterior distribution of the model parameters in a Bayesian setting. This article provides a general introduction to sequential Monte Carlo and shows how it naturally fits in system identification by giving examples of specific algorithms. The methods are illustrated on two systems: a system with two cascaded water tanks with possible overflow in both tanks and a compartmental model for the spreading of a disease.

stat.CO↗

arXiv2022

Calibration tests beyond classification

Most supervised machine learning tasks are subject to irreducible prediction errors. Probabilistic predictive models address this limitation by providing probability distributions that represent a belief over plausible targets, rather than point estimates. Such models can be a valuable tool in decision-making under uncertainty, provided that the model output is meaningful and interpretable. Calibrated models guarantee that the probabilistic predictions are neither over- nor under-confident. In the machine learning literature, different measures and statistical tests have been proposed and studied for evaluating the calibration of classification models. For regression problems, however, research has been focused on a weaker condition of calibration based on predicted quantiles for real-valued targets. In this paper, we propose the first framework that unifies calibration evaluation and tests for general probabilistic predictive models. It applies to any such model, including classification and regression models of arbitrary dimension. Furthermore, the framework generalizes existing measures and provides a more intuitive reformulation of a recently proposed framework for calibration in multi-class classification. In particular, we reformulate and generalize the kernel calibration error, its estimators, and hypothesis tests using scalar-valued kernels, and evaluate the calibration of real-valued regression problems.

stat.ML↗

arXiv2022

A Variational Perspective on Generative Flow Networks

Generative flow networks (GFNs) are a class of models for sequential sampling of composite objects, which approximate a target distribution that is defined in terms of an energy function or a reward. GFNs are typically trained using a flow matching or trajectory balance objective, which matches forward and backward transition models over trajectories. In this work, we define variational objectives for GFNs in terms of the Kullback-Leibler (KL) divergences between the forward and backward distribution. We show that variational inference in GFNs is equivalent to minimizing the trajectory balance objective when sampling trajectories from the forward model. We generalize this approach by optimizing a convex combination of the reverse- and forward KL divergence. This insight suggests variational inference methods can serve as a means to define a more general family of objectives for training generative flow networks, for example by incorporating control variates, which are commonly used in variational inference, to reduce the variance of the gradients of the trajectory balance objective. We evaluate our findings and the performance of the proposed variational objective numerically by comparing it to the trajectory balance objective on two synthetic tasks.

stat.ML↗

arXiv2022

Marginalized particle Gibbs for multiple state-space models coupled through shared parameters

We consider Bayesian inference from multiple time series described by a common state-space model (SSM) structure, but where different subsets of parameters are shared between different submodels. An important example is disease-dynamics, where parameters can be either disease or location specific. Parameter inference in these models can be improved by systematically aggregating information from the different time series, most notably for short series. Particle Gibbs (PG) samplers are an efficient class of algorithms for inference in SSMs, in particular when conjugacy can be exploited to marginalize out model parameters from the state update. We present two different PG samplers that marginalize static model parameters on-the-fly: one that updates one model at a time conditioned on the datasets for the other models, and one that concurrently updates all models by stacking them into a high-dimensional SSM. The distinctive features of each sampler make them suitable for different modelling contexts. We provide insights on when each sampler should be used and show that they can be combined to form an efficient PG sampler for a model with strong dependencies between states and parameters. The performance is illustrated on two linear-Gaussian examples and on a real-world example on the spread of mosquito-borne diseases.

stat.ME↗

arXiv2022

Scalable Deep Gaussian Markov Random Fields for General Graphs

Machine learning methods on graphs have proven useful in many applications due to their ability to handle generally structured data. The framework of Gaussian Markov Random Fields (GMRFs) provides a principled way to define Gaussian models on graphs by utilizing their sparsity structure. We propose a flexible GMRF model for general graphs built on the multi-layer structure of Deep GMRFs, originally proposed for lattice graphs only. By designing a new type of layer we enable the model to scale to large graphs. The layer is constructed to allow for efficient training using variational inference and existing software frameworks for Graph Neural Networks. For a Gaussian likelihood, close to exact Bayesian inference is available for the latent field. This allows for making predictions with accompanying uncertainty estimates. The usefulness of the proposed model is verified by experiments on a number of synthetic and real world datasets, where it compares favorably to other both Bayesian and deep learning methods.

stat.ML↗