arXiv research

PLS-Lasso integrates dimension reduction into regression for financial index tracking.

This study examines the relationship between PLS and OLS regression using eigenvalue distributions.

Motivated by the Bagging Partial Least Squares (PLS) and Principal Component Analysis (PCA) algorithms, we propose a Principal Model Analysis (PMA) method in this paper. In the proposed PMA algorithm, the PCA and the PLS are combined. In the method, multiple PLS models are trained on sub-training sets, derived from the…

New method speeds up NIR spectroscopy calibration by 400x.

Five simple soft sensor methodologies with two update conditions were compared on two experimentally-obtained datasets and one simulated dataset. The soft sensors investigated were moving window partial least squares regression (and a recursive variant), moving window random forest regression, the mean moving window of…

R-PLS improves analysis of brain functional connectivity matrices.

edPLS adds Gaussian noise to PLS regression to protect data privacy.

Proposes a new model to handle latent structure methods.

Partial Least Squares (PLS) methods have been heavily exploited to analyse the association between two blocs of data. These powerful approaches can be applied to data sets where the number of variables is greater than the number of observations and in presence of high collinearity between variables. Different sparse ve…

This paper presents regression models obtained from a process of blind prediction of peptide binding affinity from provided descriptors for several distinct datasets as part of the 2006 Comparative Evaluation of Prediction Algorithms (COEPRA) contest. This paper finds that kernel partial least squares, a nonlinear part…

Dual-sPLS improves feature selection and prediction in high-dimensional data.

Data driven soft sensor design has recently gained immense popularity, due to advances in sensory devices, and a growing interest in data mining. While partial least squares (PLS) is traditionally used in the process literature for designing soft sensors, the statistical literature has focused on sparse learners, such …

In this paper, a new descriptor selection method for selecting an optimal combination of important descriptors of sulfonamide derivatives data, named self tuned reweighted sampling (STRS), is developed. descriptors are defined as the descriptors with large absolute coefficients in a multivariate linear regression model…

The paper classifies certain PL manifolds using PL cobordism.

Functional PLS improves prediction and inference for scalar responses from functional predictors.

There have been different strategies to improve the performance of a machine learning model, e.g., increasing the depth, width, and/or nonlinearity of the model, and using ensemble learning to aggregate multiple base/weak learners in parallel or in series. This paper proposes a novel strategy called patch learning (PL)…

Proves PL cobordism category's homotopy type, analogous to smooth case.

We describe an algorithm to subdivide automatically a given set of PL n-manifolds (via coloured triangulations or, equivalently, via crystallizations) into classes whose elements are PL-homeomorphic. The algorithm, implemented in the case n=4, succeeds to solve completely the PL-homeomorphism problem among the catalogu…

Paper confirms conjecture for PL foliations of codimension 2.

Suppose M is a noncompact connected PL 2-manifold. In this paper we study the topological property of the triple (H(M)_0, H^PL(M)_0, H^PL, c(M)_0), where H(M)_0 is the identity component of the homeomorphism group {\cal H}(M) of M with the compact-open topology, and H^PL(M)_0 and H^PL, c(M)_0 are the identity component…

High-dimensional data common in genomics, proteomics, and chemometrics often contains complicated correlation structures. Recently, partial least squares (PLS) and Sparse PLS methods have gained attention in these areas as dimension reduction techniques in the context of supervised data analysis. We introduce a framewo…

Finite type invariants separate PL links in 3D space.

The purpose of this note is to scrutinize the proof of Burago and Zalgaller regarding the existence of $PL$ isometric embeddings of $PL$ compact surfaces into $\mathbb{R}^3$. We conclude that their proof does not admit a direct extension to higher dimensions. Moreover, we show that, in general, $PL$ manifolds of dimens…

There are 2^n possible resolutions of a smooth pseudodiagram with n precrossings. If we consider piecewise-linear (PL) pseudodiagrams and resolutions that themselves are PL, certain resolutions of the pseudodiagram may not exist in three-space. We investigate this situation and its impact on the weighted resolution set…

A new method for fair representation learning using PLS.

A novel dictionary-based approach for predicting functions.

Stochastic gradient methods are dominant in nonconvex optimization especially for deep models but have low asymptotical convergence due to the fixed smoothness. To address this problem, we propose a simple yet effective method for improving stochastic gradient methods named predictive local smoothness (PLS). First, we …

Study PL bordism theories with quantitative bounds on filling simplices.

Study compact PL 4-manifolds with special handle decompositions.

Smooth symplectic manifolds can be approximated by PL symplectic manifolds.

Many modern data mining applications are concerned with the analysis of datasets in which the observations are described by paired high-dimensional vectorial representations or "views". Some typical examples can be found in web mining and genomics applications. In this article we present an algorithm for data clusterin…

We extend results of Pachner and Casali to give finite sets of moves relating triangulations of PL manifolds respecting filtrations by locally flat manifolds and stratifications in which a finite family of simple local models exists for neighborhoods of strata.

Review of gem theory's interactions with Kirby diagrams and trisections.

After surveying classical notions of PL topology of the Seventies, we clarify the relation between Morse theory and its discretization by Forman. We show that PL handles theory and discrete Morse theory are equivalent, in the sense that every discrete Morse vector on some PL triangulation is also a PL handle vector, an…

Simple crystallizations are edge-coloured graphs representing PL 4-manifolds with the property that the 1-skeleton of the associated triangulation equals the 1-skeleton of a 4-simplex. In the present paper, we prove that any (simply-connected) PL $4$-manifold $M$ admitting a simple crystallization admits a special hand…

Arguments on PL,(=piecewise linear) topology work over any ordered field in the same way as over the real field, and those on differential topology do over a real closed field R in an o-minimal structure that expands (R,<,0,1,+,cdot). One of the most fundamental properties of definable sets is that a compact definable …

This paper proposes a new algorithm for Gaussian process classification based on posterior linearisation (PL). In PL, a Gaussian approximation to the posterior density is obtained iteratively using the best possible linearisation of the conditional mean of the labels and accounting for the linearisation error. PL has s…

PL-MCMC samples from normalizing flows' conditional distributions.

New examples show non-locally-flat PL-disk bounds in rational homology balls but not in integer homology balls.

Let M be a PL 2-manifold and X be a compact subpolyhedron of M and let E(X, M) denote the space of embeddings of X into M with the compact-open topology. In this paper we study an extension property of embeddings of X into M and show that the restriction map from the homeomorphism group of M to E(X, M) is a principal b…

Proves common stellar subdivisions for all PL homeomorphic polyhedra.

Paper proposes algorithms for solving nonconvex-nonconcave problems with complexity guarantees.

James McClure recently showed that the domain for the intersection pairing of PL chains on a PL manifold $M$ is a subcomplex of $C_*(M)\otimes C_*(M)$ that is quasi-isomorphic to $C_*(M)\otimes C_*(M)$ and, more generally, that the intersection pairing endows $C_*(M)$ with the structure of a partially-defined commutati…

Large PL surfaces in homology balls can have arbitrarily high genus.

Computing PL geometric category in 2D is NP-hard.

For a given polyhedron $K\subset M$ the notation $R_M(K)$ denotes a regular neighborhood of $K$ in $M$. We study the following problem: find all pairs $(m,k)$ such that if $K$ is a compact $k$-polyhedron and $M$ a PL $m$-manifold, then $R_M(fK)\cong R_M(gK)$, for each two homotopic PL embeddings $f,g:K\to M$. We prove …

For $d\geq 2$, the regular genus of a closed connected PL $d$-manifold $M$ is the least genus (resp., half of the genus) of an orientable (resp., a non-orientable) surface into which a crystallization of $M$ imbeds regularly. The regular genus of every orientable surface equals its genus, and the regular genus of every…

We generalize the PL intersection product for chains on PL manifolds and for intersection chains on PL stratified pseudomanifolds to products of locally finite chains on non-compact spaces that are natural with respect to restriction to open sets. This is necessary to sheafify the intersection product, an essential ste…