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Item Optimizing the Order of Modes in Tensor Train Decomposition(2025) Tichavský, Petr; Straka, OndřejThe tensor train (TT) is a popular way of representing high-dimensional hyper-rectangular data structures called tensors. It is widely used, for example, in quantum chemistry under the name “matrix product state”. The complexity of the TT model mainly depends on the bond dimensions that connect TT cores, constituting the model. Unlike canonical polyadic decomposition, the TT model complexity may depend on the order of the modes/indices in the data structures or the order of the core tensors in the TT, in general. This letter aims to provide methods for optimizing the order of the modes to reduce the bond dimensions. Since the number of possible orderings of the cores is exponentially high, we propose a greedy algorithm that provides a suboptimal solution. We consider three problem setups, i.e., specifications of the tensor: tensor given by a list of all its elements, tensor described by a TT model with some default order of the modes, and tensor obtained by sampling a multivariate function.
Item Discrete Time Dynamic Programming Using Tensor Trains(2025) Tichavský, Petr; Straka, Ondřej; Punčochář, IvoDiscrete time dynamic programming has many applications in decision-making and econometrics. In it, one is looking for a so-called value function that obeys a functional equation called the Bellman equation. The difficulty is that the number of variables of the value function can be very high, and a brute-force iteration of the Bellman equation is not feasible. Some authors solve this problem with deep neural networks, which have disadvantages. In this paper, we propose to handle the (sampled) value function in terms of a tensor train in a rectangular grid. Two novel techniques for the function interpolation were proposed. The decomposition has to be repeated in each Bellman iteration. Since the number of the tensor samples is still astronomically large, we propose to decompose the tensor using the TT-cross technique which only uses a fraction of the tensor elements. In this way, it is possible to find approximate solutions to the problem in dimensions where the traditional methods fail. Next, we propose a smoothing operation that may improve the convergence and a novel way of computing the approximation error and estimating the time when the iteration should be halted. The method’s performance is demonstrated in the example of the linear quadratic controller, where the ideal solution is known as the ground truth. Next, the proposed technique is applied to the problem of active fault detection, and its performance is compared to that of the neural network technique.
Item Exploring Oral History Archives Using State-of-the-Art Artificial Intelligence Methods(2025) Bulín, Martin; Švec, Jan; Ircing, Pavel; Frémund, Adam; Polák, FilipBackground: The preservation and analysis of spoken data in oral history archives, such as Holocaust testimonies, provide a vast and complex knowledge source. These archives pose unique challenges and opportunities for computational methods, particularly in self-supervised learning and information retrieval. Objective: This study explores the application of state-of-the-art artificial intelligence (AI) models, particularly transformer-based architectures, to enhance navigation and engagement with large-scale oral history testimonies. The goal is to improve accessibility while preserving the authenticity and integrity of historical records. Methods: We developed an asking questions framework utilizing a fine-tuned T5 model to generate contextually relevant questions from interview transcripts. To ensure semantic coherence, we introduced a semantic continuity model based on a BERT-like architecture trained with contrastive loss. Results: The system successfully generated contextually relevant questions from oral history testimonies, enhancing user navigation and engagement. Filtering techniques improved question quality by retaining only semantically coherent outputs, ensuring alignment with the testimony content. The approach demonstrated effectiveness in handling spontaneous, unstructured speech, with a significant improvement in question relevance compared to models trained on structured text. Applied to real-world interview transcripts, the framework balanced enrichment of user experience with preservation of historical authenticity. Conclusion: By integrating generative AI models with robust retrieval techniques, we enhance the accessibility of oral history archives while maintaining their historical integrity. This research demonstrates how AI-driven approaches can facilitate interactive exploration of vast spoken data repositories, benefiting researchers, historians and the general public.Item Lagrangian Grid-Based Filters With Application to Terrain-Aided Navigation(2025) Matoušek, Jakub; Duník, Jindřich; Straka, OndřejThe column focuses on the state estimation of discrete-time stochastic dynamic systems from noisy or incomplete measurements. State estimation has been a subject of considerable research interest for the last decades. It plays an important role in e.g. navigation, tracking, speech and image processing, fault detection, and optimal control. In this column, we introduce and explain the recent state-of-the-art efficient grid-based filtering techniques that were proven to rival the ubiquitous particle filters based on the Monte Carlo integration in terms of performance and computational complexity. Compared to the particle filters, the grid-based filters provide deterministic results with improved resilience against initialisation error and measurement outliers. The readers are guided through the design of the grid-based filters within the scope of terrain-aided navigation, which is a topical navigation solution due to the latest jamming and spoofing attacks on global navigation satellite systems. The presented algorithms and related codes in MATLAB and Python are made publicly available together with the real-world measured dataset.Item Bayesian KalmanNet: Quantifying Uncertainty in Deep Learning Augmented Kalman Filter(2025) Dahan, Yehonatan; Revach, Guy; Duník, Jindřich; Shlezinger, NirRecent years have witnessed a growing interest in tracking algorithms that augment Kalman filters (KFs) with deep neural networks (DNNs). By transforming KFs into trainable deep learning models, one can learn from data to reliably track a latent state in complex and partially known dynamics. However, unlike classic KFs, conventional DNN-based systems do not naturally provide an uncertainty measure, such as error covariance, alongside their estimates, which is crucial in various applications that rely on KF-type tracking. This work bridges this gap by studying error covariance extraction in DNN-aided KFs. We begin by characterizing how uncertainty can be extracted from existing DNN-aided algorithms and distinguishing between approaches by their ability to associate internal features with meaningful KF quantities, such as the Kalman gain and prior covariance. We then identify that uncertainty extraction from existing architectures necessitates additional domain knowledge not required for state estimation. Based on this insight, we propose Bayesian KalmanNet, a novel DNN-aided KF that integrates Bayesian deep learning techniques with the recently proposed KalmanNet and transforms the KF into a stochastic machine learning architecture. This architecture employs sampling techniques to predict error covariance reliably without requiring additional domain knowledge, while retaining KalmanNet's ability to accurately track in partially known dynamics. Our numerical study demonstrates that Bayesian KalmanNet provides accurate and reliable tracking in various scenarios representing partially known dynamic systems.Item Tensor train approximation of multivariate Gaussian density by scaling and squaring(2025) Ajgl, Jiří; Straka, OndřejTensor train decomposition is a promising tool for dealing with high dimensional arrays. Point mass filters utilise such arrays for representing probability density functions of the state. Proofs of concept of the application of the low rank decomposition have been provided in the literature. However, the application requires to design parameters, such as tensor train ranks. Since the parameters dictating the computational requirements are derived from the data according to more abstract hyper-parameters such as precision, an analysis of benchmark examples is needed for allocating resources. This paper studies the ranks in the case of Gaussian densities. The influence of correlation and the effect of rounding are discussed first. Efficiency of the density representation used by standard point mass filters is considered next. Aspects of series expansion of the Gaussian density evaluated over array are considered for the tensor train format. The growth of the ranks is illustrated on a four-dimensional example. An observation of the growth for a multi-dimensional case is made last. The lessons learned are valuable for designing efficient point mass filters. Namely, they show that at least the naive implementations of tensor decomposition methods do not break the curse of dimensionality.Item Artificial Intelligence-Aided Kalman Filters: AI-Augmented Designs for Kalman-Type Algorithms(2025) Shlezinger, Nir; Revach, Guy; Ghosh, Anubhab; Chatterjee, Saikat; Tang, Shuo; Imbiriba, Tales; Duník, Jindřich; Straka, Ondřej; Closas, Pau; Eldar, YoninaThe Kalman filter (KF) and its variants are among the most celebrated algorithms in signal processing. These methods are used for state estimation of dynamic systems by relying on mathematical representations in the form of simple state-space (SS) models, which may be crude and inaccurate descriptions of the underlying dynamics. Emerging data-centric artificial intelligence (AI) techniques tackle these tasks using deep neural networks (DNNs), which are model agnostic. Recent developments illustrate the possibility of fusing DNNs with classic Kalman-type filtering, obtaining systems that learn to track in partially known dynamics. This article provides a tutorial-style overview of design approaches for incorporating AI in aiding KF-type algorithms. We review both generic and dedicated DNN architectures suitable for state estimation and provide a systematic presentation of techniques for fusing AI tools with KFs and for leveraging partial SS modeling and data, categorizing design approaches into task oriented and SS model oriented. The usefulness of each approach in preserving the individual strengths of model-based KFs and data-driven DNNs is investigated in a qualitative and quantitative study (whose code is publicly available), illustrating the gains of hybrid model-based/data-driven designs. We also discuss existing challenges and future research directions that arise from fusing AI and Kalman-type algorithms.Item Active fault diagnosis for stochastic large scale systems under non-separable costs(2024) Straka, Ondřej; Punčochář, IvoThe paper focuses on active fault diagnosis of stochastic large-scale systems decomposed into several coupled subsystems, where the subsystem fault-free and faulty behavior is described in the multiple-model framework. In the active approach, the detector generates optimal excitation input to improve the diagnosis. This paper proposes a solution to the problems with cost functions in a generally non-separable form. Unlike the separable form, the generally non-separable form facilitates penalizing missed detections, false alerts, and incorrect, false identifications involving several subsystems simultaneously. Three approaches are proposed to treat such cost functions in the offline stage of the active fault diagnosis algorithm. Their performance is illustrated using a simple example and an elaborate example involving a power network system.Item Grid-Based Bayesian Filters With Functional Decomposition of Transient Density(2023) Tichavský, Petr; Straka, Ondřej; Duník, JindřichThe paper deals with the state estimation of nonlinear stochastic dynamic systems with special attention to grid-based Bayesian filters such as the point-mass filter (PMF) and the marginal particle filter (mPF). In the paper, a novel functional decomposition of the transient density describing the system dynamics is proposed. The decomposition approximates the transient density in a closed region. It is based on a non-negative matrix/tensor factorization and separates the density into functions of the future and current states. Such decomposition facilitates a thrifty calculation of the convolution involving the density, which is a performance bottleneck of the standard PMF/mPF implementations. The estimate quality and computational costs can be efficiently controlled by choosing an appropriate decomposition rank. The performance of the PMF with the transient density decomposition is illustrated in a terrain-aided navigation scenario and a problem involving a univariate non-stationary growth model.Item Augmented physics-based machine learning for navigation and tracking(2024) Imbiriba, Tales; Straka, Ondřej; Duník, Jindřich; Closas, PauThis article presents a survey of the use of AI/ML techniques in navigation and tracking applications, with a focus on the dynamical models typically involved in corresponding state estimation problems. When physics-based models are either not available or not able to capture the complexity of the actual dynamics, recent works explored the use of deep learning models. This article tradeoffs both models and presents promising solutions in between, whereby physics-based models are augmented by data-driven components. The article uses two target tracking examples, both with syntethic and real data, to illustrate the various choices of the models and their parameters, highlighting their benefits and challenges. Finally, the paper provides some conclusions and an outlook for future research in this relevant area.Item Identification of GNSS Measurement Error: From Time to Elevation Dependency(2023) Kost, Oliver; Duník, Jindřich; Straka, Ondřej; Daniel, OndřejThis paper deals with the identification of the GNSS measurement error properties. For this purpose, an extended version of the measurement difference method, which does not rely on knowledge of the state dynamics, is developed. The method provides elevation-dependent estimates of the pseudorange and pseudorange-rate measurement error properties in the form of both; the autocovariance function and the parametric model including the correlation time constants. The identification method is thoroughly discussed and verified using simulated and real Galileo E5b data and the identified models are utilised in the positioning solution. The identified measurement model improves the positioning accuracy by more than twenty percent.Item Design of Efficient Point-Mass Filter for Linear and Nonlinear Dynamic Models(2023) Duník, Jindřich; Matoušek, Jakub; Straka, Ondřejhis letter deals with the state estimation of nonlinear stochastic dynamic systems in the Bayesian framework. The emphasis is laid on the numerical solution to the Chapman-Kolmogorov equation by the widely-used point-mass method. It is shown, that the standard prediction step of the point-mass filter can be decomposed into two parts; advection and diffusion solution. This decomposition allows application of the fast Fourier transform, which speeds up the prediction step by several orders of magnitude making the point-mass filter attractive even for higher dimensional models. The proposed efficient point-mass filter is illustrated in a numerical simulation with available source codes and is compared with the particle filter.Item Using LSTM neural networks for cross-lingual phonetic speech segmentation with an iterative correction procedure(2024) Hanzlíček, Zdeněk; Matoušek, Jindřich; Vít, JakubThis article describes experiments on speech segmentation using long short-term memory recurrent neural networks. The main part of the paper deals with multi-lingual and cross-lingual segmentation, that is, it is performed on a language different from the one on which the model was trained. The experimental data involves large Czech, English, German, and Russian speech corpora designated for speech synthesis. For optimal multi-lingual modeling, a compact phonetic alphabet was proposed by sharing and clustering phones of particular languages. Many experiments were performed exploring various experimental conditions and data combinations. We proposed a simple procedure that iteratively adapts the inaccurate default model to the new voice/language. The segmentation accuracy was evaluated by comparison with reference segmentation created by a well-tuned hidden Markov model-based framework with additional manual corrections. The resulting segmentation was also employed in a unit selection text-to-speech system. The generated speech quality was compared with the reference segmentation by a preference listening test.Item Is it Possible to Re-educate RoBERTa? Expert-driven Machine Learning for Punctuation Correction.(2023) Machura, Jakub; Hana, Žižková; Frémund, Adam; Švec, JanAlthough Czech rule-based tools for automatic punctuation insertion rely on extensive grammar and achieve respectable precision, the pre-trained Transformers outperform rule-based systems in precision and recall (Machura et al. 2022). The Czech pre-trained RoBERTa model achieves excellent results, yet a certain level of phenomena is ignored, and the model partially makes errors. This paper aims to investigate whether it ispossible to retrain the RoBERTa language model to increase the number of sentence commas the model correctly detects. We have chosen a very specific and narrow type of sentence comma, namely the sentence comma delimiting vocative phrases, which is clearly defined in the grammar and is very often omitted by writers. The chosen approaches were further tested and evaluated on different types of texts.Item Guest Editorial for the TAES Special Section on Machine Learning Methods for Aerial and Space Positioning and Navigation(2024) Yu, Kegen; Duník, Jindřich; Braasch, Michael S.; Closas, Pau; Dovis, FabioPositioning and navigation plays a significant role in a wide range of fields, such as aerospace, defense, and transportation, especially due to the continuous performance enhancement of the four Global Navigation Satellite Systems (GNSS) [1], [2] and the advent of complementary local positioning systems [3], [4]. Nowadays, requirements on positioning and navigation are becoming stricter in areas such as reliability, accuracy, continuity, complexity, integrability, and safety to enable better location-based services. In many complex and harsh environments, it is still a demanding task (such as for aerial and space vehicles) to generate real-time valid location information and perform the desired navigation, which enables to fulfill the assigned duties [5].Item Measurement Difference Method: A Universal Tool for Noise Identification(2022) Kost, Oliver; Duník, Jindřich; Straka, OndřejThis paper deals with noise identification of a system described by the linear time-varying state-space model using correlation methods. In particular, the stress is laid on the measurement difference method (MDM) as a universal tool allowing estimation of moments and parameters of the state and measurement noises. The recent results are summarised in a common framework and the full (and weighted) MDM implementation is developed. This implementation provides unbiased and weakly consistent estimate of an arbitrary raw or central moment of the state and measurement noises. The performance of the method is illustrated in a numerical study.Item Comparison of wav2vec 2.0 models on three speech processing tasks(2024) Kunešová, Marie; Zajíc, Zbyněk; Šmídl, Luboš; Karafiát, MartinThe current state-of-the-art for various speech processing problems is a sequence-to-sequence model based on a self-attention mechanism known as transformer. The widely used wav2vec 2.0 is a self-supervised transformer model pre-trained on large amounts of unlabeled speech and then fine-tuned for a specific task. The data used for training and fine-tuning, along with the size of the transformer model, play a crucial role in both of these training steps. The most commonly used wav2vec 2.0 models are trained on relatively “clean” data from sources such as the LibriSpeech dataset, but we can expect there to be a benefit in using more realistic data gathered from a variety of acoustic conditions. However, it is not entirely clear how big the difference would be. Investigating this is the main goal of our article. To this end, we utilize wav2vec 2.0 models in three fundamental speech processing tasks: speaker change detection, voice activity detection, and overlapped speech detection, and test them on four real conversation datasets. We compare four wav2vec 2.0 models with different sizes and different data used for pre-training, and we fine-tune them either on in-domain data from the same dataset or on artificial training data created from the LibriSpeech corpus. Our results suggest that richer data that are more similar to the task domain bring better performance than a larger model.Item Enhancing reproducibility in single cell research with biocytometry: An inter-laboratory study(2024) Fikar, Pavel; Alvarez, Laura; Berne, Laura; Cienciala, Martin; Kan, Christopher; Kasl, Hynek; Luo, Mona; Novackova, Zuzana; Ordonez, Sheyla; Sramkova, Zuzana; Holubova, Monika; Lysak, Daniel; Avery, Lyndsay; Caro, Andres A.; Crowder, Roslyn N.; Diaz-Martinez, Laura A.; Donley, David W.; Giorno, Rebecca R.; Guttilla Reed, Irene K.; Hensley, Lori L.; Johnson, Kristen C.; Kim, Audrey Y.; Kim, Paul; LaGier, Adriana J.; Newman, Jamie J.; Padilla-Crespo, Elizabeth; Reyna, Nathan S.; Tsotakos, Nikolaos; Al-Saadi, Noha N.; Appleton, Tayler; Arosemena-Pickett, Ana; Bell, Braden A.; Bing, Grace; Bishop, Bre; Forde, Christa; Foster, Michael J.; Gray, Kassidy; Hasley, Bennett L.; Johnson, Kennedy; Jones, Destiny J.; LaShall, Allison C.; McGuire, Kennedy; McNaughton, Naomi; Morgan, Angelina M.; Norris, Lucas; Ossman, Landon A.; Rivera-Torres, Paollette A.; Robison, Madeline E.; Thibodaux, Kathryn; Valmond, Lescia; Georgiev, DanielBiomedicine today is experiencing a shift towards decentralized data collection, which promises enhanced reproducibility and collaboration across diverse laboratory environments. This inter-laboratory study evaluates the performance of biocytometry, a method utilizing engineered bioparticles for enumerating cells based on their surface antigen patterns. In centralized and aggregated inter-lab studies, biocytometry demonstrated significant statistical power in discriminating numbers of target cells at varying concentrations as low as 1 cell per 100,000 background cells. User skill levels varied from expert to beginner capturing a range of proficiencies. Measurement was performed in a decentralized environment without any instrument cross-calibration or advanced user training outside of a basic instruction manual. The results affirm biocytometry to be a viable solution for immunophenotyping applications demanding sensitivity as well as scalability and reproducibility and paves the way for decentralized analysis of rare cells in heterogeneous samples.Item Metaverse and AI Digital Twinning of 42SiCr Steel Alloys(MDPI, 2023) Khalaj, Omid; Jamshidi, Mohammad; Hassas, Parsa; Hosseininezhad, Marziyeh; Mašek, Bohuslav; Štádler, Ctibor; Svoboda, JiříItem Covariance Intersection fusion with element-wise partial knowledge of correlation(Elsevier, 2022) Ajgl, Jiří; Straka, OndřejPrůnik Kovariancí je pravidlo lineární fúze pro slučování odhadů. Pokud není vzájemná korelační matice chyb dvou odhadů známa, je toto pravidlo optimální ve smyslu mezí. Článek rozpracovává případ, kdy jsou některé prvky této matice známy. Zavádí techniky pro konstruování třídy horních mezí sdružené matice střední kvadratické chyby. Všechny konfigurace fúzí až čtyř odhadů jsou uvažovány výslovně. Představené techniky jsou též použitelné pro fúze více než čtyř odhadů.
