arXiv research

A parsimonious model reduces over-parameterization in skewed matrix variate mixtures.

Over the years data has become increasingly higher dimensional, which has prompted an increased need for dimension reduction techniques. This is perhaps especially true for clustering (unsupervised classification) as well as semi-supervised and supervised classification. Although dimension reduction in the area of clus…

In recent years, data have become increasingly higher dimensional and, therefore, an increased need has arisen for dimension reduction techniques for clustering. Although such techniques are firmly established in the literature for multivariate data, there is a relative paucity in the area of matrix variate, or three-w…

We propose a computationally efficient estimator, formulated as a convex program, for a broad class of non-linear regression problems that involve difference of convex (DC) non-linearities. The proposed method can be viewed as a significant extension of the "anchored regression" method formulated and analyzed in [10] f…

Proposes a low-rank bilinear pooling model for link prediction in knowledge graphs.

Bilinear MLPs offer a new way to interpret deep learning models without complex nonlinearities.

Multi-view clustering is an important and fundamental problem. Many multi-view subspace clustering methods have been proposed, and most of them assume that all views share a same coefficient matrix. However, the underlying information of multi-view data are not fully exploited under this assumption, since the coefficie…

Proposes a robust factor analysis for matrix data.

This note provides a neat and enjoyable expansion and application of the magnificent Ordentlich-Cover theory of "universal portfolios." I generalize Cover's benchmark of the best constant-rebalanced portfolio (or 1-linear trading strategy) in hindsight by considering the best bilinear trading strategy determined in hin…

Consider a smooth manifold with a smooth metric which changes bilinear type from Riemann to Lorentz on a hypersurface $Σ$ with radical tangent to $Σ$. Two natural bilinear symmetric forms appear there, and we use it to analyze the geometry of $Σ$. We show the way in which these forms control the smooth extensibility ov…

Advertising and feed ranking are essential to many Internet companies such as Facebook and Sina Weibo. Among many real-world advertising and feed ranking systems, click through rate (CTR) prediction plays a central role. There are many proposed models in this field such as logistic regression, tree based models, factor…

Recommending new items to existing users has remained a challenging problem due to absence of user's past preferences for these items. The user personalized non-collaborative methods based on item features can be used to address this item cold-start problem. These methods rely on similarities between the target item an…

Unified bounds for sketched bilinear forms in machine learning and statistics.

Efficient algorithm converges to Nash equilibrium in bilinear problems with bandit feedback.

New method improves convergence for smooth games.

We introduce the bilinear bandit problem with low-rank structure in which an action takes the form of a pair of arms from two different entity types, and the reward is a bilinear function of the known feature vectors of the arms. The unknown in the problem is a $d_1$ by $d_2$ matrix $\mathbfΘ^*$ that defines the reward…

Automatic emotion recognition (AER) is a challenging task due to the abstract concept and multiple expressions of emotion. Although there is no consensus on a definition, human emotional states usually can be apperceived by auditory and visual systems. Inspired by this cognitive process in human beings, it's natural to…

A new framework improves LSTM performance without adding more parameters.

We propose a doubly stochastic primal-dual coordinate optimization algorithm for empirical risk minimization, which can be formulated as a bilinear saddle-point problem. In each iteration, our method randomly samples a block of coordinates of the primal and dual solutions to update. The linear convergence of our method…

New algorithm reduces regret in graphical bilinear bandits.

Based on a new atomic norm, we propose a new convex formulation for sparse matrix factorization problems in which the number of nonzero elements of the factors is assumed fixed and known. The formulation counts sparse PCA with multiple factors, subspace clustering and low-rank sparse bilinear regression as potential ap…

We analyze the properties of arguably the simplest bilinear stochastic multiplicative process, proposed as a model of financial returns and of other complex systems combining both nonlinearity and multiplicative noise. By construction, it has no linear predictability (zero two-point correlation) but a certain nonlinear…

Generalization of twistor spinors to Kähler manifolds which are called Kählerian twistor spinors are considered. We find the differential equation satisfied by the bilinear forms of Kählerian twistor spinors. We show that the bilinear form equation reduces to Kählerian conformal Killing-Yano equation under special cond…

Algorithm identifies bilinear dynamical systems from noisy data.

In this paper, we propose a novel approach in order to recover a quantized matrix with missing information. We propose a regularized convex cost function composed of a log-likelihood term and a Trace norm term. The Bi-factorization approach and the Augmented Lagrangian Method (ALM) are applied to find the global minimi…

In this paper, we extend Su-Zhang's Cheeger-Mueller type theorem for symmetric bilinear torsions to manifolds with boundary in the case that the Riemannian metric and the non-degenerate symmetric bilinear form are of product structure near the boundary. Our result also extends Bruening-Ma's Cheeger-Mueller type theorem…

Identifies bilinear systems from a single trajectory with optimal sample complexity.

Generalizes Riemann's results on flat coordinates for non-symmetric bilinear forms.

The heavy-tailed distributions of corrupted outliers and singular values of all channels in low-level vision have proven effective priors for many applications such as background modeling, photometric stereo and image alignment. And they can be well modeled by a hyper-Laplacian. However, the use of such distributions g…

We present a new model, Predictive State Recurrent Neural Networks (PSRNNs), for filtering and prediction in dynamical systems. PSRNNs draw on insights from both Recurrent Neural Networks (RNNs) and Predictive State Representations (PSRs), and inherit advantages from both types of models. Like many successful RNN archi…

Drug-drug interactions (DDIs) are a major cause of preventable hospitalizations and deaths. Predicting the occurrence of DDIs helps drug safety professionals allocate investigative resources and take appropriate regulatory action promptly. Traditional DDI prediction methods predict DDIs based on the similarity between …

The theory of harmonic symmetric bilinear forms on a Riemannian manifold is an analogue of the theory of harmonic exterior differential forms on this manifold. To show this, we must consider every symmetric bilinear form on a Riemannian manifold as a one-form with values in the cotangent bundle of this manifold. In thi…

Paper reduces sample complexity for bilinear systems identification to nearly constant.

Enhances knot invariants using bilinear forms on vector spaces.

Constructs a bilinear form from a quasimorphism on symplectic manifold groups.

In this paper, we propose to employ a bank of modality-dedicated Convolutional Neural Networks (CNNs), fuse, train, and optimize them together for person classification tasks. A modality-dedicated CNN is used for each modality to extract modality-specific features. We demonstrate that, rather than spatial fusion at the…

Shape adaptor learns flexible resizing factors for neural networks.

We define a type of biquandle which is a generalization of symplectic quandles. We use the extra structure of these bilinear biquandles to define new knot and link invariants and give some examples.

Introduces and studies generalized B-opers with bilinear forms.

Study learns linear system dynamics from noisy bilinear data.

We investigate the Gram determinant of the bilinear form based on curves in a planar surface, with a focus on the disk with two holes. We prove that the determinant based on $n-1$ curves divides the determinant based on $n$ curves. Motivated by the work on Gram determinants based on curves in a disk and curves in an an…

We use the Jones-Wenzl idempotents to construct a basis of Temperley-Lieb algebra TL_n. This allows a short calculation for a Gram determinant of Lickorish's bilinear form on the Temperley-Lieb algebra.

Non-bilinear observations make optimal control harder, showing non-convex costs and non-affine optimal controllers.

This thesis is concerned with the theory of invariant bilinear differential pairings on parabolic geometries. It introduces the concept formally with the help of the jet bundle formalism and provides a detailed analysis. More precisely, after introducing the most important notations and definitions, we first of all giv…

Study examines metrics and functionals for Hodge-Dirac operator on manifolds.

BiN normalizes financial time-series for better forecasting.

Study dynamics of alternating minimization for bilinear regression under large system limits.

Novel hybrid bilinear model improves epilepsy diagnosis accuracy.