Kristiaan Pelckmans

Liang Dai, Kristiaan Pelckmans

This note addresses the question if and why the nuclear norm heuristic can recover an impulse response generated by a stable single-real-pole system, if elements of the upper-triangle of the associated Hankel matrix were given. Since the setting is deterministic, theories based on stochastic assumptions for low-rank matrix recovery do not apply here. A 'certificate' which guarantees the completion is constructed by exploring the structural information of the hidden matrix. Experimental results and discussions regarding the nuclear norm heuristic applied to a more general setting are also given.

Kristiaan Pelckmans, Moustafa Aboushady, Andreas Brosemyr

We describe a computational feather-light and intuitive, yet provably efficient algorithm, named HALFADO. HALFADO is designed for detecting suspicious events in a high-frequency stream of complex entries, based on a relatively small number of examples of human judgement. Operating a sufficiently accurate detection system is vital for {\em assisting} teams of human experts in many different areas of the modern digital society. These systems have intrinsically a far-reaching normative effect, and public knowledge of the workings of such technology should be a human right. On a conceptual level, the present approach extends one of the most classical learning algorithms for classification, inheriting its theoretical properties. It however works in a semi-supervised way integrating human and computational intelligence. On a practical level, this algorithm transcends existing approaches (expert systems) by managing and boosting their performance into a single global detector. We illustrate HALFADO's efficacy on two challenging applications: (1) for detecting {\em hate speech} messages in a flow of text messages gathered from a social media platform, and (2) for a Transaction Monitoring System (TMS) in FinTech detecting fraudulent transactions in a stream of financial transactions. This algorithm illustrates that - contrary to popular belief - advanced methods of machine learning need not require neither advanced levels of computation power nor expensive annotation efforts.

Kristiaan Pelckmans, Hong-Li Zeng

We consider the problem of learning a classifier from observed functional data. Here, each data-point takes the form of a single time-series and contains numerous features. Assuming that each such series comes with a binary label, the problem of learning to predict the label of a new coming time-series is considered. Hereto, the notion of {\em margin} underlying the classical support vector machine is extended to the continuous version for such data. The longitudinal support vector machine is also a convex optimization problem and its dual form is derived as well. Empirical results for specified cases with significance tests indicate the efficacy of this innovative algorithm for analyzing such long-term multivariate data.

Kristiaan Pelckmans, Liu Yang

This paper considers the task of learning how to make a prognosis of a patient based on his/her micro-array expression levels. The method is an application of the aggregation method as recently proposed in the literature on theoretical machine learning, and excels in its computational convenience and capability to deal with high-dimensional data. A formal analysis of the method is given, yielding rates of convergence similar to what traditional techniques obtain, while it is shown to cope well with an exponentially large set of features. Those results are supported by numerical simulations on a range of publicly available survival-micro-array datasets. It is empirically found that the proposed technique combined with a recently proposed preprocessing technique gives excellent performances.

Kristiaan Pelckmans

This paper proposes and studies a detection technique for adversarial scenarios (dubbed deterministic detection). This technique provides an alternative detection methodology in case the usual stochastic methods are not applicable: this can be because the studied phenomenon does not follow a stochastic sampling scheme, samples are high-dimensional and subsequent multiple-testing corrections render results overly conservative, sample sizes are too low for asymptotic results (as e.g. the central limit theorem) to kick in, or one cannot allow for the small probability of failure inherent to stochastic approaches. This paper instead designs a method based on insights from machine learning and online learning theory: this detection algorithm - named Online FAult Detection (FADO) - comes with theoretical guarantees of its detection capabilities. A version of the margin is found to regulate the detection performance of FADO. A precise expression is derived for bounding the performance, and experimental results are presented assessing the influence of involved quantities. A case study of scene detection is used to illustrate the approach. The technology is closely related to the linear perceptron rule, inherits its computational attractiveness and flexibility towards various extensions.

Liang Dai, Kristiaan Pelckmans

This note studies a method for the efficient estimation of a finite number of unknown parameters from linear equations, which are perturbed by Gaussian noise. In case the unknown parameters have only few nonzero entries, the proposed estimator performs more efficiently than a traditional approach. The method consists of three steps: (1) a classical Least Squares Estimate (LSE), (2) the support is recovered through a Linear Programming (LP) optimization problem which can be computed using a soft-thresholding step, (3) a de-biasing step using a LSE on the estimated support set. The main contribution of this note is a formal derivation of an associated ORACLE property of the final estimate. That is, when the number of samples is large enough, the estimate is shown to equal the LSE based on the support of the {\em true} parameters.