A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
New method infers co-expression networks robustly from multiple studies.
Simple matrix formulas for Grassmannian curvatures.
Data-aware methods for dimensionality reduction and matrix decomposition aim to find low-dimensional structure in a collection of data. Classical approaches discover such structure by learning a basis that can efficiently express the collection. Recently, "self expression", the idea of using a small subset of data vect…
The estimation of covariance matrices of gene expressions has many applications in cancer systems biology. Many gene expression studies, however, are hampered by low sample size and it has therefore become popular to increase sample size by collecting gene expression data across studies. Motivated by the traditional me…
A new method STMF improves missing value prediction using tropical semiring.
Boolean matrix factorisation aims to decompose a binary data matrix into an approximate Boolean product of two low rank, binary matrices: one containing meaningful patterns, the other quantifying how the observations can be expressed as a combination of these patterns. We introduce the OrMachine, a probabilistic genera…
Paper finds exact Hessian sharpness in deep matrix factorization.
The contribution of reducible connections to the U(N) Chern-Simons invariant of a Seifert manifold can be expressed in some cases in terms of matrix integrals. We show that the U(N) evaluation of the LMO invariant of any rational homology sphere admits a matrix model representation which agrees with the Chern-Simon…
Method cleans covariance matrices for better statistical inference.
The method integrates survival constraints into NMF for identifying survival-associated gene clusters.
We show that the objective function of conventional k-means clustering can be expressed as the Frobenius norm of the difference of a data matrix and a low rank approximation of that data matrix. In short, we show that k-means clustering is a matrix factorization problem. These notes are meant as a reference and intende…
Predicting the response of cancer cells to drugs is an important problem in pharmacogenomics. Recent efforts in generation of large scale datasets profiling gene expression and drug sensitivity in cell lines have provided a unique opportunity to study this problem. However, one major challenge is the small number of sa…
A new method to measure neural network expressiveness using tighter upper bounds.
We prove that many aspects of the differential geometry of embedded Riemannian manifolds can be formulated in terms of multi linear algebraic structures on the space of smooth functions. In particular, we find algebraic expressions for Weingarten's formula, the Ricci curvature and the Codazzi-Mainardi equations. For ma…
The ubiquitous proliferation of online social networks has led to the widescale emergence of relational graphs expressing unique patterns in link formation and descriptive user node features. Matrix Factorization and Completion have become popular methods for Link Prediction due to the low rank nature of mutual node fr…
Derives adjoint formulas for matrix operations and applies them to specific cases.
Gene expression levels in a population vary extensively across tissues. Such heterogeneity is caused by genetic variability and environmental factors, and is expected to be linked to disease development. The abundance of experimental data now enables the identification of features of gene expression profiles that are s…
The classical Matrix-Tree Theorem allows one to list the spanning trees of a graph by monomials in the expansion of the determinant of a certain matrix. We prove that in the case of three-graphs (that is, hypergraphs whose edges have exactly three vertices) the spanning trees are generated by the Pfaffian of a suitably…
We present two formulas for Chern classes of the tensor product of two vector bundles. In the first formula we consider a matrix containing Chern classes of the first bundle and we take a polynomial of this matrix with Chern classes of the second bundle as coefficients. The determinant of this expression equals the Che…
Biclustering techniques have been widely used to identify homogeneous subgroups within large data matrices, such as subsets of genes similarly expressed across subsets of patients. Mining a max-sum sub-matrix is a related but distinct problem for which one looks for a (non-necessarily contiguous) rectangular sub-matrix…
New framework for higher-order singular-value derivatives of rectangular matrices.
A very simple expression is conjectured for arbitrary colored Jones and HOMFLY polynomials of a rich -parametric family of Pretzel knots and links. The answer for the Jones and HOMFLY polynomials is fully and explicitly expressed through the Racah matrix of U_q(SU_N), and looks related to a modular transformatio…
This talk is a report on joint work with A. Vaintrob [arXiv:math.CO/0109104 and math.GT/0111102]. It is organised as follows. We begin by recalling how the classical Matrix-Tree Theorem relates two different expressions for the lowest degree coefficient of the Alexander-Conway polynomial of a link. We then state our fo…
Study of discrete period matrices on embedded graphs, relating to Riemann surfaces.
New MPNNs match 2-WL, faster distinguishing graphs.
We introduce a construction of the differential calculus on the quantum supergroup GL. We obtain two differential calculi, respectively, associated with the left and right Cartan-Maurer one-forms. We also obtain the quantum superalgebra of GL. Although all of the structures we obtain are der…
We introduce a novel Bayesian hybrid matrix factorisation model (HMF) for data integration, based on combining multiple matrix factorisation methods, that can be used for in- and out-of-matrix prediction of missing values. The model is very general and can be used to integrate many datasets across different entity type…
New insights into matrix factorization show strict saddles have bounded eigenvalues.
Scalable Gaussian processes with latent Kronecker structure for large datasets.
The stability and robustness of compact schemes for parabolic PDEs are analyzed.
Machine learning and geostatistics are powerful mathematical frameworks for modeling spatial data. Both approaches, however, suffer from poor scaling of the required computational resources for large data applications. We present the Stochastic Local Interaction (SLI) model, which employs a local representation to impr…
New model predicts drug effects across various cell types using causal imputation.
New guarantees for recovering matrices as low-rank plus sparse from fewer measurements.
Scattering theory on Riemann surfaces with explicit matrix and generalized period mappings.
New distribution simplifies covariance matrix inference.
Recently, the Weisfeiler-Lehman (WL) graph isomorphism test was used to measure the expressive power of graph neural networks (GNN). It was shown that the popular message passing GNN cannot distinguish between graphs that are indistinguishable by the 1-WL test (Morris et al. 2018; Xu et al. 2019). Unfortunately, many s…
Algorithm recovers sparse PCA support from incomplete data.
We introduce two methods for estimating the density matrix for a quantum system: Quantum Maximum Likelihood and Quantum Variational Inference. In these methods, we construct a variational family to model the density matrix of a mixed quantum state. We also introduce quantum flows, the quantum analog of normalizing flow…
sgdGMF efficiently estimates generalized matrix factorization models for single-cell RNA sequencing data.
Graphical notation simplifies complex polynomial constraints in linear models.
A new method combines multiple cancer datasets to improve analysis.
We classify isotopy classes of irreducible Heegaard splittings of solvmanifolds. If the monodromy of the solvmanifold can be expressed as a 2 x 2 matrix with 0 in the lower right hand corner (as always is true when the absolute value of the trace is 3), then any irreducible splitting is strongly irreducible and of genu…
In this paper we study general Schatten- quasi-norm (SPQN) regularized matrix minimization problems. In particular, we first introduce a class of first-order stationary points for them, and show that the first-order stationary points introduced in [11] for an SPQN regularized minimization problem are equiva…
We consider the problem of covariance matrix estimation in the presence of latent variables. Under suitable conditions, it is possible to learn the marginal covariance matrix of the observed variables via a tractable convex program, where the concentration matrix of the observed variables is decomposed into a sparse ma…
We calculate Blanchfield pairings of 3-manifolds. In particular, we give a formula for the Blanchfield pairing of a fibred 3-manifold and we give a new proof that the Blanchfield pairing of a knot can be expressed in terms of a Seifert matrix.
Proposes a convex method to estimate GGMs with covariates.
We describe a novel way of representing a symbolic knowledge base (KB) called a sparse-matrix reified KB. This representation enables neural modules that are fully differentiable, faithful to the original semantics of the KB, expressive enough to model multi-hop inferences, and scalable enough to use with realistically…
WGNN learns graph representations from incomplete attribute data.