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A large class of non-smooth practical optimization problems can be written as minimization of a sum of smooth and partly smooth functions. We examine such structured problems which also depend on a parameter vector and study the problem of…
A new data-driven bilateral generalized two-dimensional quaternion principal component analysis (BiG2DQPCA) is presented to extract the features of matrix samples from both row and column directions. This general framework directly works on…
In this paper, we explore methods of robustly extracting fiducial facial feature points - an important process for numerous facial image processing tasks. We consider various methods to first detect face, then facial features and finally…
Motivated by the following two observations: 1) people are aging differently under different conditions for changeable facial attributes, e.g., skin color may become darker when working outside, and 2) it needs to keep some unchanged facial…
Algorithms for partition refinement are actively studied for a variety of systems, often with the optimisation called Hopcroft's trick. However, the low-level description of those algorithms in the literature often obscures the essence of…
Existing facial analysis systems have been shown to yield biased results against certain demographic subgroups. Due to its impact on society, it has become imperative to ensure that these systems do not discriminate based on gender,…
We discuss issues of problem formulation for algorithms in real algebraic geometry, focussing on quantifier elimination by cylindrical algebraic decomposition. We recall how the variable ordering used can have a profound effect on both…
The standard practice in Generative Adversarial Networks (GANs) discards the discriminator during sampling. However, this sampling method loses valuable information learned by the discriminator regarding the data distribution. In this work,…
Adversarial Imitation Learning alternates between learning a discriminator -- which tells apart expert's demonstrations from generated ones -- and a generator's policy to produce trajectories that can fool this discriminator. This…
A computational fluid dynamics code is differentiated using algorithmic differentiation (AD) in both tangent and adjoint modes. The two novelties of the present approach are 1) the adjoint code is obtained by letting the AD tool Tapenade…
Face synthesis has been a fascinating yet challenging problem in computer vision and machine learning. Its main research effort is to design algorithms to generate photo-realistic face images via given semantic domain. It has been a crucial…
An effective numerical method is presented for optimizing model parameters that can be applied to any type of system of non-linear equations and any number of data-points, which does not require explicit formulation of the objective…
In this paper, we analyze the numerics of common algorithms for training Generative Adversarial Networks (GANs). Using the formalism of smooth two-player games we analyze the associated gradient vector field of GAN training objectives. Our…
In this paper, we consider spectral approximation of fractional differential equations (FDEs). A main ingredient of our approach is to define a new class of generalized Jacobi functions (GJFs), which is intrinsically related to fractional…
Current works formulate facial action unit (AU) recognition as a supervised learning problem, requiring fully AU-labeled facial images during training. It is challenging if not impossible to provide AU annotations for large numbers of…
Ren et al. recently introduced a method for aggregating multiple decision trees into a strong predictor by interpreting a path taken by a sample down each tree as a binary vector and performing linear regression on top of these vectors…
A sequential quadratic optimization algorithm is proposed for solving smooth nonlinear equality constrained optimization problems in which the objective function is defined by an expectation of a stochastic function. The algorithmic…
We describe a hidden surface removal algorithm for two-dimensional layered scenes built from arbitrary primitives, particularly suited to interaction and animation in rich scenes (for example, in illustration). The method makes use of a…
The repeated solution of large-scale optimization problems arises frequently in process systems engineering tasks. Decomposition-based solution methods have been widely used to reduce the corresponding computational time, yet their…
The two underlying requirements of face age progression, i.e. aging accuracy and identity permanence, are not well studied in the literature. In this paper, we present a novel generative adversarial network based approach. It separately…