Related papers: A kernel function for Signal Temporal Logic formul…
We propose an interval extension of Signal Temporal Logic (STL) called Interval Signal Temporal Logic (\ISTL). Given an STL formula, we consider an interval inclusion function for each of its predicates. Then, we use minimal inclusion…
This paper proposes a new nonlinear approach for additive functional regression with functional response based on kernel methods along with some slight reformulation and implementation of the linear regression and the spectral additive…
Continuous representations of logic formulae allow us to integrate symbolic knowledge into data-driven learning algorithms. If such embeddings are semantically consistent, i.e. if similar specifications are mapped into nearby vectors, they…
In this paper, we propose a neuro-symbolic framework called weighted Signal Temporal Logic Neural Network (wSTL-NN) that combines the characteristics of neural networks and temporal logics. Weighted Signal Temporal Logic (wSTL) formulas are…
In most adaptive signal processing applications, system linearity is assumed and adaptive linear filters are thus used. The traditional class of supervised adaptive filters rely on error-correction learning for their adaptive capability.…
Linear autoregressive models serve as basic representations of discrete time stochastic processes. Different attempts have been made to provide non-linear versions of the basic autoregressive process, including different versions based on…
Signal processing tasks as fundamental as sampling, reconstruction, minimum mean-square error interpolation and prediction can be viewed under the prism of reproducing kernel Hilbert spaces. Endowing this vantage point with contemporary…
This paper presents a technique, named STLCG, to compute the quantitative semantics of Signal Temporal Logic (STL) formulas using computation graphs. STLCG provides a platform which enables the incorporation of logical specifications into…
This study intends to introduce kernel mean embedding of probability measures over infinite-dimensional separable Hilbert spaces induced by functional response statistical models. The embedded function represents the concentration of…
Signal Temporal Logic (STL) inference seeks to extract human-interpretable rules from time-series data, but existing methods lack formal confidence guarantees for the inferred rules. Conformal prediction (CP) is a technique that can provide…
In many applications of machine learning, a large number of variables are considered. Motivated by machine learning of interacting particle systems, we consider the situation when the number of input variables goes to infinity. First, we…
In this paper, we characterize Probabilistic Principal Component Analysis in Hilbert spaces and demonstrate how the optimal solution admits a representation in dual space. This allows us to develop a generative framework for kernel methods.…
In this paper, we discuss the convergence analysis of the conjugate gradient-based algorithm for the functional linear model in the reproducing kernel Hilbert space framework, utilizing early stopping results in regularization against…
We present a mathematical programming-based method for model predictive control of cyber-physical systems subject to signal temporal logic (STL) specifications. We describe the use of STL to specify a wide range of properties of these…
Kernel methods, being supported by a well-developed theory and coming with efficient algorithms, are among the most popular and successful machine learning techniques. From a mathematical point of view, these methods rest on the concept of…
Quantum kernel methods leverage a kernel function computed by embedding input information into the Hilbert space of a quantum system. However, large Hilbert spaces can hinder generalization capability, and the scalability of quantum kernels…
In this article, a novel approach to learning a complex function which can be written as the system of linear equations is introduced. This learning is grounded upon the observation that solving the system of linear equations by a…
The role of kernels is central to machine learning. Motivated by the importance of power-law distributions in statistical modeling, in this paper, we propose the notion of power-law kernels to investigate power-laws in learning problem. We…
In this work, we consider the problem of learning nonlinear operators that correspond to discrete-time nonlinear dynamical systems with inputs. Given an initial state and a finite input trajectory, such operators yield a finite output…
The integration of cyber-physical systems (CPS) into everyday life raises the critical necessity of ensuring their safety and reliability. An important step in this direction is requirement mining, i.e. inferring formally specified system…