Matej Petković

Urh Primožič, Ljupčo Todorovski, Matej Petković

Probabilistic context-free grammars have a long-term record of use as generative models in machine learning and symbolic regression. When used for symbolic regression, they generate algebraic expressions. We define the latter as equivalence classes of strings derived by grammar and address the problem of calculating the probability of deriving a given expression with a given grammar. We show that the problem is undecidable in general. We then present specific grammars for generating linear, polynomial, and rational expressions, where algorithms for calculating the probability of a given expression exist. For those grammars, we design algorithms for calculating the exact probability and efficient approximation with arbitrary precision.

Andrej Bauer, Matej Petković, Ljupčo Todorovski

We introduce MLFMF, a collection of data sets for benchmarking recommendation systems used to support formalization of mathematics with proof assistants. These systems help humans identify which previous entries (theorems, constructions, datatypes, and postulates) are relevant in proving a new theorem or carrying out a new construction. Each data set is derived from a library of formalized mathematics written in proof assistants Agda or Lean. The collection includes the largest Lean~4 library Mathlib, and some of the largest Agda libraries: the standard library, the library of univalent mathematics Agda-unimath, and the TypeTopology library. Each data set represents the corresponding library in two ways: as a heterogeneous network, and as a list of s-expressions representing the syntax trees of all the entries in the library. The network contains the (modular) structure of the library and the references between entries, while the s-expressions give complete and easily parsed information about every entry. We report baseline results using standard graph and word embeddings, tree ensembles, and instance-based learning algorithms. The MLFMF data sets provide solid benchmarking support for further investigation of the numerous machine learning approaches to formalized mathematics. The methodology used to extract the networks and the s-expressions readily applies to other libraries, and is applicable to other proof assistants. With more than $250\,000$ entries in total, this is currently the largest collection of formalized mathematical knowledge in machine learnable format.

Urh Primožič, Blaž Škrlj, Sašo Džeroski et al.

The need for learning from unlabeled data is increasing in contemporary machine learning. Methods for unsupervised feature ranking, which identify the most important features in such data are thus gaining attention, and so are their applications in studying high throughput biological experiments or user bases for recommender systems. We propose FRANe (Feature Ranking via Attribute Networks), an unsupervised algorithm capable of finding key features in given unlabeled data set. FRANe is based on ideas from network reconstruction and network analysis. FRANe performs better than state-of-the-art competitors, as we empirically demonstrate on a large collection of benchmarks. Moreover, we provide the time complexity analysis of FRANe further demonstrating its scalability. Finally, FRANe offers as the result the interpretable relational structures used to derive the feature importances.

Blaž Škrlj, Matej Petkovič

Contemporary natural language processing (NLP) revolves around learning from latent document representations, generated either implicitly by neural language models or explicitly by methods such as doc2vec or similar. One of the key properties of the obtained representations is their dimension. Whilst the commonly adopted dimensions of 256 and 768 offer sufficient performance on many tasks, it is many times unclear whether the default dimension is the most suitable choice for the subsequent downstream learning tasks. Furthermore, representation dimensions are seldom subject to hyperparameter tuning due to computational constraints. The purpose of this paper is to demonstrate that a surprisingly simple and efficient recursive compression procedure can be sufficient to both significantly compress the initial representation, but also potentially improve its performance when considering the task of text classification. Having smaller and less noisy representations is the desired property during deployment, as orders of magnitude smaller models can significantly reduce the computational overload and with it the deployment costs. We propose CoRe, a straightforward, representation learner-agnostic framework suitable for representation compression. The CoRe's performance is showcased and studied on a collection of 17 real-life corpora from biomedical, news, social media, and literary domains. We explored CoRe's behavior when considering contextual and non-contextual document representations, different compression levels, and 9 different compression algorithms. Current results based on more than 100,000 compression experiments indicate that recursive Singular Value Decomposition offers a very good trade-off between the compression efficiency and performance, making CoRe useful in many existing, representation-dependent NLP pipelines.

Matej Petković, Luke Lucas, Tomaž Stepišnik et al.

The Mars Express (MEX) spacecraft has been orbiting Mars since 2004. The operators need to constantly monitor its behavior and handle sporadic deviations (outliers) from the expected patterns of measurements of quantities that the satellite is sending to Earth. In this paper, we analyze the patterns of the electrical power consumption of MEX's thermal subsystem, that maintains the spacecraft's temperature at the desired level. The consumption is not constant, but should be roughly periodic in the short term, with the period that corresponds to one orbit around Mars. By using long short-term memory neural networks, we show that the consumption pattern is more irregular than expected, and successfully detect such irregularities, opening possibility for automatic outlier detection on MEX in the future.

Ana Kostovska, Matej Petković, Tomaž Stepišnik et al.

We present GalaxAI - a versatile machine learning toolbox for efficient and interpretable end-to-end analysis of spacecraft telemetry data. GalaxAI employs various machine learning algorithms for multivariate time series analyses, classification, regression and structured output prediction, capable of handling high-throughput heterogeneous data. These methods allow for the construction of robust and accurate predictive models, that are in turn applied to different tasks of spacecraft monitoring and operations planning. More importantly, besides the accurate building of models, GalaxAI implements a visualisation layer, providing mission specialists and operators with a full, detailed and interpretable view of the data analysis process. We show the utility and versatility of GalaxAI on two use-cases concerning two different spacecraft: i) analysis and planning of Mars Express thermal power consumption and ii) predicting of INTEGRAL's crossings through Van Allen belts.

Blaž Škrlj, Sašo Džeroski, Nada Lavrač et al.

Feature ranking has been widely adopted in machine learning applications such as high-throughput biology and social sciences. The approaches of the popular Relief family of algorithms assign importances to features by iteratively accounting for nearest relevant and irrelevant instances. Despite their high utility, these algorithms can be computationally expensive and not-well suited for high-dimensional sparse input spaces. In contrast, recent embedding-based methods learn compact, low-dimensional representations, potentially facilitating down-stream learning capabilities of conventional learners. This paper explores how the Relief branch of algorithms can be adapted to benefit from (Riemannian) manifold-based embeddings of instance and target spaces, where a given embedding's dimensionality is intrinsic to the dimensionality of the considered data set. The developed ReliefE algorithm is faster and can result in better feature rankings, as shown by our evaluation on 20 real-life data sets for multi-class and multi-label classification tasks. The utility of ReliefE for high-dimensional data sets is ensured by its implementation that utilizes sparse matrix algebraic operations. Finally, the relation of ReliefE to other ranking algorithms is studied via the Fuzzy Jaccard Index.

Matej Petković, Dragi Kocev, Blaž Škrlj et al.

In this work, we propose two novel (groups of) methods for unsupervised feature ranking and selection. The first group includes feature ranking scores (Genie3 score, RandomForest score) that are computed from ensembles of predictive clustering trees. The second method is URelief, the unsupervised extension of the Relief family of feature ranking algorithms. Using 26 benchmark data sets and 5 baselines, we show that both the Genie3 score (computed from the ensemble of extra trees) and the URelief method outperform the existing methods and that Genie3 performs best overall, in terms of predictive power of the top-ranked features. Additionally, we analyze the influence of the hyper-parameters of the proposed methods on their performance, and show that for the Genie3 score the highest quality is achieved by the most efficient parameter configuration. Finally, we propose a way of discovering the location of the features in the ranking, which are the most relevant in reality.

Nikolaos Nikolaou, Ingo P. Waldmann, Angelos Tsiaras et al.

The last decade has witnessed a rapid growth of the field of exoplanet discovery and characterisation. However, several big challenges remain, many of which could be addressed using machine learning methodology. For instance, the most prolific method for detecting exoplanets and inferring several of their characteristics, transit photometry, is very sensitive to the presence of stellar spots. The current practice in the literature is to identify the effects of spots visually and correct for them manually or discard the affected data. This paper explores a first step towards fully automating the efficient and precise derivation of transit depths from transit light curves in the presence of stellar spots. The methods and results we present were obtained in the context of the 1st Machine Learning Challenge organized for the European Space Agency's upcoming Ariel mission. We first present the problem, the simulated Ariel-like data and outline the Challenge while identifying best practices for organizing similar challenges in the future. Finally, we present the solutions obtained by the top-5 winning teams, provide their code and discuss their implications. Successful solutions either construct highly non-linear (w.r.t. the raw data) models with minimal preprocessing -deep neural networks and ensemble methods- or amount to obtaining meaningful statistics from the light curves, constructing linear models on which yields comparably good predictive performance.

Matej Petković, Sašo Džeroski, Dragi Kocev

The data made available for analysis are becoming more and more complex along several directions: high dimensionality, number of examples and the amount of labels per example. This poses a variety of challenges for the existing machine learning methods: coping with dataset with a large number of examples that are described in a high-dimensional space and not all examples have labels provided. For example, when investigating the toxicity of chemical compounds there are a lot of compounds available, that can be described with information rich high-dimensional representations, but not all of the compounds have information on their toxicity. To address these challenges, we propose semi-supervised learning of feature ranking. The feature rankings are learned in the context of classification and regression as well as in the context of structured output prediction (multi-label classification, hierarchical multi-label classification and multi-target regression). To the best of our knowledge, this is the first work that treats the task of feature ranking within the semi-supervised structured output prediction context. More specifically, we propose two approaches that are based on tree ensembles and the Relief family of algorithms. The extensive evaluation across 38 benchmark datasets reveals the following: Random Forests perform the best for the classification-like tasks, while for the regression-like tasks Extra-PCTs perform the best, Random Forests are the most efficient method considering induction times across all tasks, and semi-supervised feature rankings outperform their supervised counterpart across a majority of the datasets from the different tasks.

Matej Petković, Blaž Škrlj, Dragi Kocev et al.

We propose Fuzzy Jaccard Index (FUJI) -- a scale-invariant score for assessment of the similarity between two ranked/ordered lists. FUJI improves upon the Jaccard index by incorporating a membership function which takes into account the particular ranks, thus producing both more stable and more accurate similarity estimates. We provide theoretical insights into the properties of the FUJI score as well as propose an efficient algorithm for computing it. We also present empirical evidence of its performance on different synthetic scenarios. Finally, we demonstrate its utility in a typical machine learning setting -- comparing feature ranking lists relevant to a given machine learning task. In real-life, and in particular high-dimensional domains, where only a small percentage of the whole feature space might be relevant, a robust and confident feature ranking leads to interpretable findings as well as efficient computation and good predictive performance. In such cases, FUJI correctly distinguishes between existing feature ranking approaches, while being more robust and efficient than the benchmark similarity scores.

Blaž Škrlj, Sašo Džeroski, Nada Lavrač et al.

Black-box neural network models are widely used in industry and science, yet are hard to understand and interpret. Recently, the attention mechanism was introduced, offering insights into the inner workings of neural language models. This paper explores the use of attention-based neural networks mechanism for estimating feature importance, as means for explaining the models learned from propositional (tabular) data. Feature importance estimates, assessed by the proposed Self-Attention Network (SAN) architecture, are compared with the established ReliefF, Mutual Information and Random Forest-based estimates, which are widely used in practice for model interpretation. For the first time we conduct scale-free comparisons of feature importance estimates across algorithms on ten real and synthetic data sets to study the similarities and differences of the resulting feature importance estimates, showing that SANs identify similar high-ranked features as the other methods. We demonstrate that SANs identify feature interactions which in some cases yield better predictive performance than the baselines, suggesting that attention extends beyond interactions of just a few key features and detects larger feature subsets relevant for the considered learning task.

Matej Petković, Redouane Boumghar, Martin Breskvar et al.

The thermal subsystem of the Mars Express (MEX) spacecraft keeps the on-board equipment within its pre-defined operating temperatures range. To plan and optimize the scientific operations of MEX, its operators need to estimate in advance, as accurately as possible, the power consumption of the thermal subsystem. The remaining power can then be allocated for scientific purposes. We present a machine learning pipeline for efficiently constructing accurate predictive models for predicting the power of the thermal subsystem on board MEX. In particular, we employ state-of-the-art feature engineering approaches for transforming raw telemetry data, in turn used for constructing accurate models with different state-of-the-art machine learning methods. We show that the proposed pipeline considerably improve our previous (competition-winning) work in terms of time efficiency and predictive performance. Moreover, while achieving superior predictive performance, the constructed models also provide important insight into the spacecraft's behavior, allowing for further analyses and optimal planning of MEX's operation.