Related papers: $\ell_1$ Adaptive Trend Filter via Fast Coordinate…
We propose TrendSegment, a methodology for detecting multiple change-points corresponding to linear trend changes in one dimensional data. A core ingredient of TrendSegment is a new Tail-Greedy Unbalanced Wavelet transform: a conditionally…
We introduce an online outlier detection algorithm to detect outliers in a sequentially observed data stream. For this purpose, we use a two-stage filtering and hedging approach. In the first stage, we construct a multi-modal probability…
Trend filtering simplifies complex time series data by applying smoothness to filter out noise while emphasizing proximity to the original data. However, existing trend filtering methods fail to reflect abrupt changes in the trend due to…
Impulsed noise outliers are data points that differs significantly from other observations.They are generally removed from the data set through local regression or Kalman filter algorithm.However, these methods, or their generalizations,…
This paper describes a methodology for detecting anomalies from sequentially observed and potentially noisy data. The proposed approach consists of two main elements: (1) {\em filtering}, or assigning a belief or likelihood to each…
In this article, we discuss various implementation of L1 filtering in order to detect some properties of noisy signals. This filter consists of using a L1 penalty condition in order to obtain the filtered signal composed by a set of…
The leading workhorse of anomaly (and attack) detection in the literature has been residual-based detectors, where the residual is the discrepancy between the observed output provided by the sensors (inclusive of any tampering along the…
This paper presents the construction of a particle filter, which incorporates elements inspired by genetic algorithms, in order to achieve accelerated adaptation of the estimated posterior distribution to changes in model parameters.…
We study additive models built with trend filtering, i.e., additive models whose components are each regularized by the (discrete) total variation of their $k$th (discrete) derivative, for a chosen integer $k \geq 0$. This results in $k$th…
In addition to ever-present thermal noise, various communication and sensor systems can contain significant amounts of interference with outlier (e.g. impulsive) characteristics. Such outlier noise can be efficiently mitigated in real-time…
Recent research has demonstrated that transformers, particularly linear attention models, implicitly execute gradient-descent-like algorithms on data provided in-context during their forward inference step. However, their capability in…
This work develops techniques for the sequential detection and location estimation of transient changes in the volatility (standard deviation) of time series data. In particular, we introduce a class of change detection algorithms based on…
The unscented Kalman filter is an algorithm capable of handling nonlinear scenarios. Uncertainty in process noise covariance may decrease the filter estimation performance or even lead to its divergence. Therefore, it is important to adjust…
Adaptive filters are at the core of many signal processing applications, ranging from acoustic noise supression to echo cancelation, array beamforming, channel equalization, to more recent sensor network applications in surveillance, target…
When signals are measured through physical sensors, they are perturbed by noise. To reduce noise, low-pass filters are commonly employed in order to attenuate high frequency components in the incoming signal, regardless if they come from…
As contemporary software-intensive systems reach increasingly large scale, it is imperative that failure detection schemes be developed to help prevent costly system downtimes. A promising direction towards the construction of such schemes…
The sparsity of natural signals and images in a transform domain or dictionary has been extensively exploited in several applications such as compression, denoising and inverse problems. More recently, data-driven adaptation of synthesis…
Change point detection is a crucial aspect of analyzing time series data, as the presence of a change point indicates an abrupt and significant change in the process generating the data. While many algorithms for the problem of change point…
In this paper we investigate the problem of detecting dynamically evolving signals. We model the signal as an $n$ dimensional vector that is either zero or has $s$ non-zero components. At each time step $t\in \mathbb{N}$ the non-zero…
A recently discovered universal rank-based matrix method to extract trends from noisy time series is described in [1] but the formula for the output matrix elements, implemented there as an open-access supplement MATLAB computer code, is…