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Publications (10 of 56) Show all publications
Mattsson, P., Zachariah, D. & Stoica, P. (2023). Analysis of the Minimum-Norm Least-Squares Estimator and Its Double-Descent Behavior [Lecture Notes]. IEEE signal processing magazine (Print), 40(3), 39-75
Open this publication in new window or tab >>Analysis of the Minimum-Norm Least-Squares Estimator and Its Double-Descent Behavior [Lecture Notes]
2023 (English)In: IEEE signal processing magazine (Print), ISSN 1053-5888, E-ISSN 1558-0792, Vol. 40, no 3, p. 39-75Article in journal (Refereed) Published
Abstract [en]

Linear regression models have a wide range of applications in statistics, signal processing, and machine learning. In this Lecture Notes column we will examine the performance of the least-squares (LS) estimator with a focus on the case when there are more parameters than training samples, which is often overlooked in textbooks on estimation.

Place, publisher, year, edition, pages
IEEE, 2023
Keywords
Least squares methods, Linear regression, Estimation, Machine learning, Signal processing, Behavioral sciences
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:uu:diva-504033 (URN)10.1109/MSP.2023.3242083 (DOI)000981974000005 ()
Available from: 2023-06-28 Created: 2023-06-28 Last updated: 2023-06-28Bibliographically approved
Wang, Z., Stoica, P., Zachariah, D., Babu, P. & Yang, Z. (2023). Min-Max Probe Placement and Extended Relaxation Estimation Method for Processing Blade Tip Timing Signals. IEEE Transactions on Instrumentation and Measurement, 72, Article ID 3535509.
Open this publication in new window or tab >>Min-Max Probe Placement and Extended Relaxation Estimation Method for Processing Blade Tip Timing Signals
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2023 (English)In: IEEE Transactions on Instrumentation and Measurement, ISSN 0018-9456, E-ISSN 1557-9662, Vol. 72, article id 3535509Article in journal (Refereed) Published
Abstract [en]

Measuring blade displacement using blade tip timing (BTT) enables nonintrusive monitoring of rotating blades and their vibration frequencies. The average sampling frequency of BTT is the product of the number of measurement probes and rotational frequency, which is usually far less than the blade natural frequency due to the limited number of probes. The pattern of the aliasing that arises from under-sampling is rather complex under uneven probe placement. In this article, we consider a probe placement design that is based on minimizing the maximum sidelobe level of the spectral window to suppress the aliasing frequencies in the spectrum. Based on a signal model containing both asynchronous and synchronous sinusoids, we then develop an extended version of the RELAX method (ERELAX) to estimate their parameters simultaneously. Model order selection rules are also used to determine the number of asynchronous sinusoids. The frequency ambiguity that arises from periodic nonuniform sampling (PNS) is also discussed based on the convolution in the frequency domain. Numerical simulations and results of a curved-blade experiment show that the proposed method has a mean squared estimation error less than 25% of that of two state-of-the-art methods (Block-OMP and MUSIC), requires 40% of the data length needed by the latter methods to achieve the same estimation accuracy, and has the smallest standard deviation of the reconstruction errors. Simulation codes are available at https://github.com/superjdg/RELAX_BTT.

Place, publisher, year, edition, pages
Institute of Electrical and Electronics Engineers (IEEE), 2023
Keywords
Probes, Blades, Vibrations, Vibration measurement, Frequency synchronization, Time-frequency analysis, Frequency estimation, Blade tip timing (BTT), frequency ambiguity, min-max placement, model order selection, relax
National Category
Signal Processing
Identifiers
urn:nbn:se:uu:diva-516652 (URN)10.1109/TIM.2023.3324671 (DOI)001093394400004 ()
Funder
Swedish Research Council, 2017-04610Swedish Research Council, 2016-06079Swedish Research Council, 2021-05022
Available from: 2023-11-28 Created: 2023-11-28 Last updated: 2023-11-28Bibliographically approved
Ek, S., Zachariah, D., Johansson, F. D. & Stoica, P. (2023). Off-Policy Evaluation with Out-of-Sample Guarantees. Transactions on Machine Learning Research
Open this publication in new window or tab >>Off-Policy Evaluation with Out-of-Sample Guarantees
2023 (English)In: Transactions on Machine Learning Research, E-ISSN 2835-8856Article in journal (Refereed) Published
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:uu:diva-519244 (URN)
Available from: 2024-01-04 Created: 2024-01-04 Last updated: 2024-01-09Bibliographically approved
Osama, M., Zachariah, D., Stoica, P. & Schön, T. B. (2023). Online Learning for Prediction via Covariance Fitting: Computation, Performance and Robustness. Transactions on Machine Learning Research
Open this publication in new window or tab >>Online Learning for Prediction via Covariance Fitting: Computation, Performance and Robustness
2023 (English)In: Transactions on Machine Learning Research, E-ISSN 2835-8856Article in journal (Refereed) Published
Abstract [en]

We consider the online learning of linear smoother predictors based on a covariance model of the outcomes. To control its degrees of freedom in an appropriate manner, the covariance model parameters are often learned using cross-validation or maximum-likelihood techniques. However, neither technique is suitable when training data arrives in a streaming fashion. Here we consider a covariance-fitting method to learn the model parameters, initially used  in spectral estimation. We show that this results in a computation efficient online learning method in which the resulting predictor can be updated sequentially. We prove that, with high probability, its out-of-sample error approaches the minimum achievable level at root-$n$ rate. Moreover, we show that the resulting predictor enjoys two different robustness properties. First, it minimizes the out-of-sample error with respect to the least favourable distribution within a given Wasserstein distance from the empirical distribution. Second, it is robust against errors in the covariate training data. We illustrate the performance of the proposed method in a numerical experiment.

Place, publisher, year, edition, pages
Transactions on Machine Learning Research, 2023
National Category
Probability Theory and Statistics Engineering and Technology
Identifiers
urn:nbn:se:uu:diva-472451 (URN)
Available from: 2022-04-11 Created: 2022-04-11 Last updated: 2024-01-08Bibliographically approved
Mattsson, P., Zachariah, D. & Stoica, P. (2023). Regularized Linear Regression via Covariance Fitting. IEEE Transactions on Signal Processing, 71, 1175-1183
Open this publication in new window or tab >>Regularized Linear Regression via Covariance Fitting
2023 (English)In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 71, p. 1175-1183Article in journal (Refereed) Published
Abstract [en]

The linear minimum mean-square error estimator (LMMSE) can be viewed as a solution to a certain regularized least-squares problem formulated using model covariance matrices. However, the appropriate parameters of the model covariance matrices are unknown in many applications. This raises the question: how should we choose them using only the data? Using data-adaptive matrices obtained via the covariance fitting SPICE-methodology, we show that the empirical LMMSE is equivalent to tuned versions of various known regularized estimators - such as ridge regression, LASSO, and regularized least absolute deviation - depending on the chosen covariance structures. These theoretical results unify several important estimators under a common umbrella. Furthermore, through a number of numerical examples we show that the regularization parameters obtained via covariance fitting are close to optimal for a range of different signal conditions.

Place, publisher, year, edition, pages
IEEE, 2023
Keywords
Estimation theory, parameter estimation
National Category
Probability Theory and Statistics Signal Processing
Identifiers
urn:nbn:se:uu:diva-502506 (URN)10.1109/TSP.2023.3263363 (DOI)000976047000002 ()
Funder
Swedish Research Council, 621-2016-06079Swedish Research Council, 2018-05040Swedish Research Council, 2021-05022
Available from: 2023-05-29 Created: 2023-05-29 Last updated: 2023-05-29Bibliographically approved
Cockshott, P. & Zachariah, D. (2022). A shift from the problematic of "transformation". WORLD REVIEW OF POLITICAL ECONOMY, 12(4), 463-471
Open this publication in new window or tab >>A shift from the problematic of "transformation"
2022 (English)In: WORLD REVIEW OF POLITICAL ECONOMY, ISSN 2042-891X, Vol. 12, no 4, p. 463-471Article in journal (Refereed) Published
Abstract [en]

We examine the paradigm shift from that of the transformation model to that of stochastic profit models. Some of the anomalies undermining the transformation model are given graphically. In the last two sections we present volume II of Capital as an alternative starting point for thinking about the relation between value and price.

Place, publisher, year, edition, pages
Pluto Press, 2022
Keywords
reproduction-scheme, paradigm, profit rate
National Category
Economics
Identifiers
urn:nbn:se:uu:diva-487623 (URN)10.13169/worlrevipoliecon.12.4.0463 (DOI)000864514400004 ()
Available from: 2022-11-04 Created: 2022-11-04 Last updated: 2022-11-04Bibliographically approved
Ek, S., Zachariah, D. & Stoica, P. (2022). Learning Pareto-Efficient Decisions with Confidence. In: Camps-Valls, G Ruiz, FJR Valera, I (Ed.), International Conference on Artificial Intelligence and Statistics: . Paper presented at International Conference on Artificial Intelligence and Statistics, MAR 28-30, 2022, ELECTR NETWORK (pp. 9969-9981). JMLR-JOURNAL MACHINE LEARNING RESEARCH, 151
Open this publication in new window or tab >>Learning Pareto-Efficient Decisions with Confidence
2022 (English)In: International Conference on Artificial Intelligence and Statistics / [ed] Camps-Valls, G Ruiz, FJR Valera, I, JMLR-JOURNAL MACHINE LEARNING RESEARCH , 2022, Vol. 151, p. 9969-9981Conference paper, Published paper (Refereed)
Abstract [en]

The paper considers the problem of multi-objective decision support when outcomes are uncertain. We extend the concept of Pareto-efficient decisions to take into account the uncertainty of decision outcomes across varying contexts. This enables quantifying trade-offs between decisions in terms of tail outcomes that are relevant in safety-critical applications. We propose a method for learning efficient decisions with statistical confidence, building on results from the conformal prediction literature. The method adapts to weak or nonexistent context covariate overlap and its statistical guarantees are evaluated using both synthetic and real data.

Place, publisher, year, edition, pages
JMLR-JOURNAL MACHINE LEARNING RESEARCH, 2022
Series
Proceedings of Machine Learning Research, ISSN 2640-3498
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:uu:diva-487888 (URN)000841852304022 ()
Conference
International Conference on Artificial Intelligence and Statistics, MAR 28-30, 2022, ELECTR NETWORK
Funder
Knut and Alice Wallenberg FoundationSwedish Research Council, 2018-05040Swedish Research Council, 2021-05022
Available from: 2022-11-14 Created: 2022-11-14 Last updated: 2023-04-03Bibliographically approved
Kharyton, V. & Zachariah, D. (2021). Advanced Processing of a Blade Vibratory Response Obtained With Tip Timing Method Using Hyperparameter-Free Sparse Estimation Method. In: : . Paper presented at ASME Turbo Expo 2021: Turbomachinery Technical Conference and Exposition. , 85031
Open this publication in new window or tab >>Advanced Processing of a Blade Vibratory Response Obtained With Tip Timing Method Using Hyperparameter-Free Sparse Estimation Method
2021 (English)Conference paper, Published paper (Refereed)
National Category
Signal Processing
Identifiers
urn:nbn:se:uu:diva-492803 (URN)
Conference
ASME Turbo Expo 2021: Turbomachinery Technical Conference and Exposition
Available from: 2023-01-10 Created: 2023-01-10 Last updated: 2023-01-13Bibliographically approved
Osama, M., Zachariah, D., Dwivedi, S. & Stoica, P. (2021). Robust localization in wireless networks from corrupted signals. EURASIP Journal on Advances in Signal Processing, 2021(1), Article ID 79.
Open this publication in new window or tab >>Robust localization in wireless networks from corrupted signals
2021 (English)In: EURASIP Journal on Advances in Signal Processing, ISSN 1687-6172, E-ISSN 1687-6180, Vol. 2021, no 1, article id 79Article in journal (Refereed) Published
Abstract [en]

We address the problem of timing-based localization in wireless networks, when an unknown fraction of data is corrupted by non-ideal propagation conditions. While timing-based techniques can enable accurate localization, they are sensitive to corrupted data. We develop a robust method that is applicable to a range of localization techniques, including time-of-arrival, time-difference-of-arrival and time-difference in schedule-based transmissions. The method is distribution-free, is computationally efficient and requires only an upper bound on the fraction of corrupted data, thus obviating distributional assumptions on the corrupting noise. The robustness of the method is demonstrated in numerical experiments.

Place, publisher, year, edition, pages
SpringerSPRINGER, 2021
Keywords
Localization, Robustness, Wireless networks, Time-of-arrival, Time-difference-of-arrival
National Category
Signal Processing
Identifiers
urn:nbn:se:uu:diva-456481 (URN)10.1186/s13634-021-00786-8 (DOI)000695828100001 ()
Funder
Swedish Research Council, 2016-06079Swedish Research Council, 2017-04610Swedish Research Council, 2018-05040
Available from: 2021-10-21 Created: 2021-10-21 Last updated: 2024-01-15Bibliographically approved
Liu, X., Ngai, E. & Zachariah, D. (2021). Scalable Belief Updating for Urban Air Quality Modeling and Prediction. ACM/IMS Transactions on Data Science, 2(1), 1-19
Open this publication in new window or tab >>Scalable Belief Updating for Urban Air Quality Modeling and Prediction
2021 (English)In: ACM/IMS Transactions on Data Science, E-ISSN 2577-3224, Vol. 2, no 1, p. 1-19Article in journal (Refereed) Published
Abstract [en]

Air pollution is one of the major concerns in global urbanization. Data science can help to understand the dynamics of air pollution and build reliable statistical models to forecast air pollution levels. To achieve these goals, one needs to learn the statistical models which can capture the dynamics from the historical data and predict air pollution in the future. Furthermore, the large size and heterogeneity of today’s big urban data pose significant challenges on the scalability and flexibility of the statistical models. In this work, we present a scalable belief updating framework that is able to produce reliable predictions, using over millions of historical hourly air pollutant and meteorology records. We also present a non-parametric approach to learn the statistical model which reveals interesting periodical dynamics and correlations of the dataset. Based on the scalable belief update framework and the non-parametric model learning approach, we propose an iterative update algorithm to accelerate Gaussian process, which is notorious for its prohibitive computation with large input data. Finally, we demonstrate how to integrate information from heterogeneous data by regarding the beliefs produced by other models as the informative prior. Numerical examples and experimental results are presented to validate the proposed method.

Place, publisher, year, edition, pages
Association for Computing Machinery (ACM), 2021
National Category
Signal Processing
Identifiers
urn:nbn:se:uu:diva-492802 (URN)10.1145/3402903 (DOI)
Available from: 2023-01-10 Created: 2023-01-10 Last updated: 2023-06-02Bibliographically approved
Projects
Counterfactual Prediction Methods for Heterogeneous Populations [2018-05040_VR]; Uppsala University
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0002-6698-0166

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