Magnus Jansson

Mohammad Reza Gholami, Magnus Jansson, Erik G. Ström et al.

In many fields, and especially in the medical and social sciences and in recommender systems, data are gathered through clinical studies or targeted surveys. Participants are generally reluctant to respond to all questions in a survey or they may lack information to respond adequately to some questions. The data collected from these studies tend to lead to linear regression models where the regression vectors are only known partially: some of their entries are either missing completely or replaced randomly by noisy values. In this work, assuming missing positions are replaced by noisy values, we examine how a connected network of agents, with each one of them subjected to a stream of data with incomplete regression information, can cooperate with each other through local interactions to estimate the underlying model parameters in the presence of missing data. We explain how to adjust the distributed diffusion through (de)regularization in order to eliminate the bias introduced by the incomplete model. We also propose a technique to recursively estimate the (de)regularization parameter and examine the performance of the resulting strategy. We illustrate the results by considering two applications: one dealing with a mental health survey and the other dealing with a household consumption survey.

Aihui Liu, Magnus Jansson

We study local sensitivity of structured ARX-based data-driven predictive control. Although predictor estimation is linear in the ARX parameters, the lifted multi-step predictor used in MPC depends on them implicitly, which complicates both uncertainty propagation and task-aware regularization. We derive a local first-order linearization of this implicit predictor map. The resulting Jacobian yields both an approximate control-relevant prediction uncertainty term and a task-dependent sensitivity metric for shaping kernel regularization. Numerical results show that the proposed analysis is most useful in weak-excitation regimes, where baseline SS regularization already provides substantial robustness gains and the proposed sensitivity shaping yields a further smaller improvement.

Martin Sundin, Arun Venkitaraman, Magnus Jansson et al.

Graphs are naturally sparse objects that are used to study many problems involving networks, for example, distributed learning and graph signal processing. In some cases, the graph is not given, but must be learned from the problem and available data. Often it is desirable to learn sparse graphs. However, making a graph highly sparse can split the graph into several disconnected components, leading to several separate networks. The main difficulty is that connectedness is often treated as a combinatorial property, making it hard to enforce in e.g. convex optimization problems. In this article, we show how connectedness of undirected graphs can be formulated as an analytical property and can be enforced as a convex constraint. We especially show how the constraint relates to the distributed consensus problem and graph Laplacian learning. Using simulated and real data, we perform experiments to learn sparse and connected graphs from data.

Martin Sundin, Cristian R. Rojas, Magnus Jansson et al.

We develop latent variable models for Bayesian learning based low-rank matrix completion and reconstruction from linear measurements. For under-determined systems, the developed methods are shown to reconstruct low-rank matrices when neither the rank nor the noise power is known a-priori. We derive relations between the latent variable models and several low-rank promoting penalty functions. The relations justify the use of Kronecker structured covariance matrices in a Gaussian based prior. In the methods, we use evidence approximation and expectation-maximization to learn the model parameters. The performance of the methods is evaluated through extensive numerical simulations.

Martin Sundin, Saikat Chatterjee, Magnus Jansson

Using a Bayesian approach, we consider the problem of recovering sparse signals under additive sparse and dense noise. Typically, sparse noise models outliers, impulse bursts or data loss. To handle sparse noise, existing methods simultaneously estimate the sparse signal of interest and the sparse noise of no interest. For estimating the sparse signal, without the need of estimating the sparse noise, we construct a robust Relevance Vector Machine (RVM). In the RVM, sparse noise and ever present dense noise are treated through a combined noise model. The precision of combined noise is modeled by a diagonal matrix. We show that the new RVM update equations correspond to a non-symmetric sparsity inducing cost function. Further, the combined modeling is found to be computationally more efficient. We also extend the method to block-sparse signals and noise with known and unknown block structures. Through simulations, we show the performance and computation efficiency of the new RVM in several applications: recovery of sparse and block sparse signals, housing price prediction and image denoising.

Martin Sundin, Saikat Chatterjee, Magnus Jansson et al.

In this paper we develop a new Bayesian inference method for low rank matrix reconstruction. We call the new method the Relevance Singular Vector Machine (RSVM) where appropriate priors are defined on the singular vectors of the underlying matrix to promote low rank. To accelerate computations, a numerically efficient approximation is developed. The proposed algorithms are applied to matrix completion and matrix reconstruction problems and their performance is studied numerically.