Teemu Roos

Tomi Silander, Janne Leppä-aho, Elias Jääsaari et al.

We introduce an information theoretic criterion for Bayesian network structure learning which we call quotient normalized maximum likelihood (qNML). In contrast to the closely related factorized normalized maximum likelihood criterion, qNML satisfies the property of score equivalence. It is also decomposable and completely free of adjustable hyperparameters. For practical computations, we identify a remarkably accurate approximation proposed earlier by Szpankowski and Weinberger. Experiments on both simulated and real data demonstrate that the new criterion leads to parsimonious models with good predictive accuracy.

Ioanna Bouri, Fanni Franssila, Markku Alho et al.

Topological analysis of the magnetic field in simulated plasmas allows the study of various physical phenomena in a wide range of settings. One such application is magnetic reconnection, a phenomenon related to the dynamics of the magnetic field topology, which is difficult to detect and characterize in three dimensions. We propose a scalable pipeline for topological data analysis and spatiotemporal graph representation of three-dimensional magnetic vector fields. We demonstrate our methods on simulations of the Earth's magnetosphere produced by Vlasiator, a supercomputer-scale Vlasov theory-based simulation for near-Earth space. The purpose of this work is to challenge the machine learning community to explore graph-based machine learning approaches to address a largely open scientific problem with wide-ranging potential impact.

Daniel Holmberg, Ivan Zaitsev, Markku Alho et al.

Hybrid-Vlasov simulations resolve ion-kinetic effects in the solar wind-magnetosphere interaction, but even 5D (2D + 3V) configurations are computationally expensive. We show that graph-based machine learning emulators can learn the spatiotemporal evolution of electromagnetic fields and lower order moments of ion velocity distribution in the near-Earth space environment from four 5D Vlasiator runs performed with identical steady solar wind conditions. The initial ion number density is systematically varied, while the grid spacing is held constant, to scan the ratio of the characteristic ion skin depth to the numerical grid size. Using a graph neural network (GNN) operating on the 2D spatial simulation grid comprising 670k cells, we demonstrate that both a deterministic forecasting model (Graph-FM) and a probabilistic ensemble forecasting model (Graph-EFM) based on a latent variable formulation are capable of producing accurate predictions of future plasma states. A divergence penalty is incorporated to encourage divergence-freeness in the magnetic fields. For the probabilistic model, a continuous ranked probability score objective is added to improve the calibration of the ensemble forecasts. The trained emulators achieve over two orders of magnitude speedup per time step on a single GPU compared to 100 CPU Vlasiator simulations. Most forecasted fields have Pearson correlations above 0.95 at 50 seconds lead time. However, we find that fields that exhibit near-zero degenerate distributions in the 5D setting are more challenging for the emulator to maintain high correlations for. Overall, these results demonstrate that GNNs provide a viable framework for rapid ensemble generation in hybrid-Vlasov modeling and highlight promising directions for future work.

Elias Jääsaari, Ville Hyvönen, Teemu Roos

Multi-vector representations generated by late interaction models, such as ColBERT, enable superior retrieval quality compared to single-vector representations in information retrieval applications. In multi-vector retrieval systems, both queries and documents are encoded using one embedding for each token, and similarity between queries and documents is measured by the MaxSim similarity measure. However, the improved recall of multi-vector retrieval comes at the expense of significantly increased latency. This necessitates designing efficient approximate nearest neighbor search (ANNS) algorithms for multi-vector search. In this work, we introduce LEMUR, a simple-yet-efficient framework for multi-vector similarity search. LEMUR consists of two consecutive problem reductions: We first formulate multi-vector similarity search as a supervised learning problem that can be solved using a one-hidden-layer neural network. Second, we reduce inference under this model to single-vector similarity search in its latent space, which enables the use of existing single-vector ANNS methods for speeding up retrieval. In addition to performance evaluation on ColBERTv2 embeddings, we evaluate LEMUR on embeddings generated by modern multi-vector text models and multi-vector visual document retrieval models. LEMUR is an order of magnitude faster than earlier multi-vector similarity search methods.

Daniel Holmberg, Joel Oskarsson, Erik Larsson et al.

Ocean dynamics are inherently chaotic, yet existing machine learning ocean models produce only deterministic forecasts. We introduce Njord, a probabilistic data-driven model for ocean forecasting, applicable to both global and regional domains. Njord combines a deep latent variable framework with a graph neural network architecture, enabling sampling each forecast step in a single forward pass. We apply Njord globally at 0.25° resolution and regionally to the Baltic Sea at 2 km resolution. To scale to these large ocean grids we introduce K-means cluster meshes that adapt to irregular sea surface geometry. Experiments demonstrate strong performance on both domains compared to deterministic machine learning baselines, while also providing uncertainty estimates from the sampled ensemble forecasts. On the global OceanBench benchmark, Njord achieves the lowest errors on average across upper-ocean variables when evaluated against real-world observations, with the largest improvements in surface temperature prediction.

Elias Jääsaari, Ville Hyvönen, Matteo Ceccarello et al.

Approximate nearest neighbor (ANN) search is a performance-critical component of many machine learning pipelines. Rigorous benchmarking is essential for evaluating the performance of vector indexes for ANN search. However, the datasets of the existing benchmarks are no longer representative of the current applications of ANN search. Hence, there is an urgent need for an up-to-date set of benchmarks. To this end, we introduce Vector Index Benchmark for Embeddings (VIBE), an open source project for benchmarking ANN algorithms. VIBE contains a pipeline for creating benchmark datasets using dense embedding models characteristic of modern applications, such as retrieval-augmented generation (RAG). To replicate real-world workloads, we also include out-of-distribution (OOD) datasets where the queries and the corpus are drawn from different distributions. We use VIBE to conduct a comprehensive evaluation of SOTA vector indexes, benchmarking 21 implementations on 12 in-distribution and 6 out-of-distribution datasets.

Jussi Määttä, Viacheslav Bazaliy, Jyri Kimari et al.

Many applications, especially in physics and other sciences, call for easily interpretable and robust machine learning techniques. We propose a fully gradient-based technique for training radial basis function networks with an efficient and scalable open-source implementation. We derive novel closed-form optimization criteria for pruning the models for continuous as well as binary data which arise in a challenging real-world material physics problem. The pruned models are optimized to provide compact and interpretable versions of larger models based on informed assumptions about the data distribution. Visualizations of the pruned models provide insight into the atomic configurations that determine atom-level migration processes in solid matter; these results may inform future research on designing more suitable descriptors for use with machine learning algorithms.

Elias Jääsaari, Ville Hyvönen, Teemu Roos

Approximate nearest neighbor (ANN) search is a key component in many modern machine learning pipelines; recent use cases include retrieval-augmented generation (RAG) and vector databases. Clustering-based ANN algorithms, that use score computation methods based on product quantization (PQ), are often used in industrial-scale applications due to their scalability and suitability for distributed and disk-based implementations. However, they have slower query times than the leading graph-based ANN algorithms. In this work, we propose a new supervised score computation method based on the observation that inner product approximation is a multivariate (multi-output) regression problem that can be solved efficiently by reduced-rank regression. Our experiments show that on modern high-dimensional data sets, the proposed reduced-rank regression (RRR) method is superior to PQ in both query latency and memory usage. We also introduce LoRANN, a clustering-based ANN library that leverages the proposed score computation method. LoRANN is competitive with the leading graph-based algorithms and outperforms the state-of-the-art GPU ANN methods on high-dimensional data sets.

Daniel Holmberg, Emanuela Clementi, Teemu Roos

Accurate ocean forecasting systems are vital for understanding marine dynamics, which play a crucial role in environmental management and climate adaptation strategies. Traditional numerical solvers, while effective, are computationally expensive and time-consuming. Recent advancements in machine learning have revolutionized weather forecasting, offering fast and energy-efficient alternatives. Building on these advancements, we introduce SeaCast, a neural network designed for high-resolution, medium-range ocean forecasting. SeaCast employs a graph-based framework to effectively handle the complex geometry of ocean grids and integrates external forcing data tailored to the regional ocean context. Our approach is validated through experiments at a high spatial resolution using the operational numerical model of the Mediterranean Sea provided by the Copernicus Marine Service, along with both numerical and data-driven atmospheric forcings.

Daniel Holmberg, Ivan Zaitsev, Markku Alho et al.

Accurate space weather forecasting is crucial for protecting our increasingly digital infrastructure. Hybrid-Vlasov models, like Vlasiator, offer physical realism beyond that of current operational systems, but are too computationally expensive for real-time use. We introduce a graph-based neural emulator trained on Vlasiator data to autoregressively predict near-Earth space conditions driven by an upstream solar wind. We show how to achieve both fast deterministic forecasts and, by using a generative model, produce ensembles to capture forecast uncertainty. This work demonstrates that machine learning offers a way to add uncertainty quantification capability to existing space weather prediction systems, and make hybrid-Vlasov simulation tractable for operational use.

Daniel Holmberg, Manu Airaksinen, Viviana Marchi et al.

Reliable methods for the neurodevelopmental assessment of infants are essential for early detection of problems that may need prompt interventions. Spontaneous motor activity, or 'kinetics', is shown to provide a powerful surrogate measure of upcoming neurodevelopment. However, its assessment is by and large qualitative and subjective, focusing on visually identified, age-specific gestures. In this work, we introduce Kinetic Age (KA), a novel data-driven metric that quantifies neurodevelopmental maturity by predicting an infant's age based on their movement patterns. KA offers an interpretable and generalizable proxy for motor development. Our method leverages 3D video recordings of infants, processed with pose estimation to extract spatio-temporal series of anatomical landmarks, which are released as a new openly available dataset. These data are modeled using adaptive graph convolutional networks, able to capture the spatio-temporal dependencies in infant movements. We also show that our data-driven approach achieves improvement over traditional machine learning baselines based on manually engineered features.

Aqsa Saeed Qureshi, Teemu Roos

Several machine learning techniques for accurate detection of skin cancer from medical images have been reported. Many of these techniques are based on pre-trained convolutional neural networks (CNNs), which enable training the models based on limited amounts of training data. However, the classification accuracy of these models still tends to be severely limited by the scarcity of representative images from malignant tumours. We propose a novel ensemble-based CNN architecture where multiple CNN models, some of which are pre-trained and some are trained only on the data at hand, along with auxiliary data in the form of metadata associated with the input images, are combined using a meta-learner. The proposed approach improves the model's ability to handle limited and imbalanced data. We demonstrate the benefits of the proposed technique using a dataset with 33126 dermoscopic images from 2056 patients. We evaluate the performance of the proposed technique in terms of the F1-measure, area under the ROC curve (AUC-ROC), and area under the PR-curve (AUC-PR), and compare it with that of seven different benchmark methods, including two recent CNN-based techniques. The proposed technique compares favourably in terms of all the evaluation metrics.

Ville Hyvönen, Elias Jääsaari, Teemu Roos

Both supervised and unsupervised machine learning algorithms have been used to learn partition-based index structures for approximate nearest neighbor (ANN) search. Existing supervised algorithms formulate the learning task as finding a partition in which the nearest neighbors of a training set point belong to the same partition element as the point itself, so that the nearest neighbor candidates can be retrieved by naive lookup or backtracking search. We formulate candidate set selection in ANN search directly as a multilabel classification problem where the labels correspond to the nearest neighbors of the query point, and interpret the partitions as partitioning classifiers for solving this task. Empirical results suggest that the natural classifier based on this interpretation leads to strictly improved performance when combined with any unsupervised or supervised partitioning strategy. We also prove a sufficient condition for consistency of a partitioning classifier for ANN search, and illustrate the result by verifying this condition for chronological $k$-d trees.

Peter Grünwald, Teemu Roos

This is an up-to-date introduction to and overview of the Minimum Description Length (MDL) Principle, a theory of inductive inference that can be applied to general problems in statistics, machine learning and pattern recognition. While MDL was originally based on data compression ideas, this introduction can be read without any knowledge thereof. It takes into account all major developments since 2007, the last time an extensive overview was written. These include new methods for model selection and averaging and hypothesis testing, as well as the first completely general definition of {\em MDL estimators}. Incorporating these developments, MDL can be seen as a powerful extension of both penalized likelihood and Bayesian approaches, in which penalization functions and prior distributions are replaced by more general luckiness functions, average-case methodology is replaced by a more robust worst-case approach, and in which methods classically viewed as highly distinct, such as AIC vs BIC and cross-validation vs Bayes can, to a large extent, be viewed from a unified perspective.

Elias Jääsaari, Ville Hyvönen, Teemu Roos

Approximate nearest neighbor algorithms are used to speed up nearest neighbor search in a wide array of applications. However, current indexing methods feature several hyperparameters that need to be tuned to reach an acceptable accuracy--speed trade-off. A grid search in the parameter space is often impractically slow due to a time-consuming index-building procedure. Therefore, we propose an algorithm for automatically tuning the hyperparameters of indexing methods based on randomized space-partitioning trees. In particular, we present results using randomized k-d trees, random projection trees and randomized PCA trees. The tuning algorithm adds minimal overhead to the index-building process but is able to find the optimal hyperparameters accurately. We demonstrate that the algorithm is significantly faster than existing approaches, and that the indexing methods used are competitive with the state-of-the-art methods in query time while being faster to build.

Janne Leppä-aho, Santeri Räisänen, Xiao Yang et al.

We propose a method for learning Markov network structures for continuous data without invoking any assumptions about the distribution of the variables. The method makes use of previous work on a non-parametric estimator for mutual information which is used to create a non-parametric test for multivariate conditional independence. This independence test is then combined with an efficient constraint-based algorithm for learning the graph structure. The performance of the method is evaluated on several synthetic data sets and it is shown to learn considerably more accurate structures than competing methods when the dependencies between the variables involve non-linearities.

Janne Leppä-aho, Johan Pensar, Teemu Roos et al.

We propose a Bayesian approximate inference method for learning the dependence structure of a Gaussian graphical model. Using pseudo-likelihood, we derive an analytical expression to approximate the marginal likelihood for an arbitrary graph structure without invoking any assumptions about decomposability. The majority of the existing methods for learning Gaussian graphical models are either restricted to decomposable graphs or require specification of a tuning parameter that may have a substantial impact on learned structures. By combining a simple sparsity inducing prior for the graph structures with a default reference prior for the model parameters, we obtain a fast and easily applicable scoring function that works well for even high-dimensional data. We demonstrate the favourable performance of our approach by large-scale comparisons against the leading methods for learning non-decomposable Gaussian graphical models. A theoretical justification for our method is provided by showing that it yields a consistent estimator of the graph structure.

Ville Hyvönen, Teemu Pitkänen, Sotiris Tasoulis et al.

Efficient index structures for fast approximate nearest neighbor queries are required in many applications such as recommendation systems. In high-dimensional spaces, many conventional methods suffer from excessive usage of memory and slow response times. We propose a method where multiple random projection trees are combined by a novel voting scheme. The key idea is to exploit the redundancy in a large number of candidate sets obtained by independently generated random projections in order to reduce the number of expensive exact distance evaluations. The method is straightforward to implement using sparse projections which leads to a reduced memory footprint and fast index construction. Furthermore, it enables grouping of the required computations into big matrix multiplications, which leads to additional savings due to cache effects and low-level parallelization. We demonstrate by extensive experiments on a wide variety of data sets that the method is faster than existing partitioning tree or hashing based approaches, making it the fastest available technique on high accuracy levels.

Andrew Barron, Teemu Roos, Kazuho Watanabe

The normalized maximized likelihood (NML) provides the minimax regret solution in universal data compression, gambling, and prediction, and it plays an essential role in the minimum description length (MDL) method of statistical modeling and estimation. Here we show that the normalized maximum likelihood has a Bayes-like representation as a mixture of the component models, even in finite samples, though the weights of linear combination may be both positive and negative. This representation addresses in part the relationship between MDL and Bayes modeling. This representation has the advantage of speeding the calculation of marginals and conditionals required for coding and prediction applications.

Michael Sherman, Gradeigh Clark, Yulong Yang et al.

This paper studies the security and memorability of free-form multitouch gestures for mobile authentication. Towards this end, we collected a dataset with a generate-test-retest paradigm where participants (N=63) generated free-form gestures, repeated them, and were later retested for memory. Half of the participants decided to generate one-finger gestures, and the other half generated multi-finger gestures. Although there has been recent work on template-based gestures, there are yet no metrics to analyze security of either template or free-form gestures. For example, entropy-based metrics used for text-based passwords are not suitable for capturing the security and memorability of free-form gestures. Hence, we modify a recently proposed metric for analyzing information capacity of continuous full-body movements for this purpose. Our metric computed estimated mutual information in repeated sets of gestures. Surprisingly, one-finger gestures had higher average mutual information. Gestures with many hard angles and turns had the highest mutual information. The best-remembered gestures included signatures and simple angular shapes. We also implemented a multitouch recognizer to evaluate the practicality of free-form gestures in a real authentication system and how they perform against shoulder surfing attacks. We conclude the paper with strategies for generating secure and memorable free-form gestures, which present a robust method for mobile authentication.