Related papers: Additive Models with Trend Filtering
The convergence analysis for least-squares finite element methods led to various adaptive mesh-refinement strategies: Collective marking algorithms driven by the built-in a posteriori error estimator or an alternative explicit…
We introduce a new analysis of an adaptive mixture method that combines outputs of two constituent filters running in parallel to model an unknown desired signal. This adaptive mixture is shown to achieve the mean square error (MSE)…
Extracting the underlying trend signal is a crucial step to facilitate time series analysis like forecasting and anomaly detection. Besides noise signal, time series can contain not only outliers but also abrupt trend changes in real-world…
In many contexts involving ranked preferences, agents submit partial orders over available alternatives. Statistical models often treat these as marginal in the space of total orders, but this approach overlooks information contained in the…
Identifying the unknown underlying trend of a given noisy signal is extremely useful for a wide range of applications. The number of potential trends might be exponential, which can be computationally exhaustive even for short signals.…
In \cite{liu2022practical}, a general algorithm is developed to efficiently obtain the best accuracy using the regular refinement. The adaptive refinement allows for obtaining an accuracy with a smaller number of DoFs compared with 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 combine high-dimensional factor models with fractional integration methods and derive models where nonstationary, potentially cointegrated data of different persistence is modelled as a function of common fractionally integrated factors.…
Additive models and generalized additive models are effective semiparametric tools for multidimensional data. In this article we propose an online smoothing backfitting method for generalized additive models with local polynomial smoothers.…
We consider a non-linear filtering problem, whereby the signal obeys the stochastic Navier-Stokes equations and is observed through a linear mapping with additive noise. The setup is relevant to data assimilation for numerical weather…
Nonlinear adaptive filters often show some sparse behavior due to the fact that not all the coefficients are equally useful for the modeling of any nonlinearity. Recently, a class of proportionate algorithms has been proposed for nonlinear…
The ability to automatically discover interpretable mathematical models from data could forever change how we model soft matter systems. For convex discovery problems with a unique global minimum, model discovery is well-established. It…
In model selection problems for machine learning, the desire for a well-performing model with meaningful structure is typically expressed through a regularized optimization problem. In many scenarios, however, the meaningful structure is…
Feature selection can facilitate the learning of mixtures of discrete random variables as they arise, e.g. in crowdsourcing tasks. Intuitively, not all workers are equally reliable but, if the less reliable ones could be eliminated, then…
The filtering-clustering models, including trend filtering and convex clustering, have become an important source of ideas and modeling tools in machine learning and related fields. The statistical guarantee of optimal solutions in these…
Nonparametric regression models with locally stationary covariates have received increasing interest in recent years. As a nice relief of "curse of dimensionality" induced by large dimension of covariates, additive regression model is…
We provide a flexible framework for selecting among a class of additive partial linear models that allows both linear and nonlinear additive components. In practice, it is challenging to determine which additive components should be…
In this study, we propose a novel motif-based approach for unsupervised textile anomaly detection that combines the benefits of traditional convolutional neural networks with those of an unsupervised learning paradigm. It consists of five…
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…
Modeling the temporal behavior of data is of primordial importance in many scientific and engineering fields. Baseline methods assume that both the dynamic and observation equations follow linear-Gaussian models. However, there are many…