Gould and Robinson [SIAM J. Optim., 20 (2010), pp. 2023–2048] proved global convergence of a second derivative SQP method for minimizing the exact 1-merit function for a fixed value of the penalty parameter. This result required the properties of a so-called Cauchy step, which was itself computed from a so-called predictor step. In addition, they allowed for the additional computation of a vari...

This paper describes our work for the “Emotion in Music” task of MediaEval 2015. The goal of the task is predicting affective content of a song. The affective content is presented in terms of valence and arousal criterions, which are shown in a timecontinuous fashion. We adopt deep recurrent neural network (DRNN) to predict the valence and arousal for each moment of a song, and Limited-Memory-B...

We propose a new stochastic L-BFGS algorithm and prove a linear convergence rate for strongly convex and smooth functions. Our algorithm draws heavily from a recent stochastic variant of L-BFGS proposed in Byrd et al. (2014) as well as a recent approach to variance reduction for stochastic gradient descent from Johnson and Zhang (2013). We demonstrate experimentally that our algorithm performs ...

We take a new look at parameter estimation for Gaussian Mixture Models (GMMs). In particular, we propose using Riemannian manifold optimization as a powerful counterpart to Expectation Maximization (EM). An out-of-the-box invocation of manifold optimization, however, fails spectacularly: it converges to the same solution but vastly slower. Driven by intuition from manifold convexity, we then pr...

We present a two-stage method for obtaining both phase and object estimates from phase-diversity time series data. In the first stage, the phases are estimated for each time frame using the limited memory BFGS method. In the second stage, an algorithm that incorporates a nonnegativity constraint as well prior knowledge of data noise statistics is used to obtain an estimate of the object being o...

How to computationally model human performance in complex cognitive and multi-task scenarios has become an important yet challenging question for human performance modelling and simulation. This paper reports the work that develops an integrated cognitive architecture for this purpose. The resulting architecture – queueing network-adaptive control of thought rational (QN-ACTR) – is an integrati...

We introduce a quasi-Newton method with block updates called Block BFGS. We show that this method, performed with inexact Armijo-Wolfe line searches, converges globally and superlinearly under the same convexity assumptions as BFGS. We also show that Block BFGS is globally convergent to a stationary point when applied to non-convex functions with bounded Hessian, and discuss other modifications...

A common approach for minimizing a smooth nonlinear function is to employ finite-difference approximations the gradient. While this can be easily performed when no error present within evaluations, noisy, optimal choice requires information about noise level and higher-order derivatives of function, which often unavailable. Given we propose bisection search finding interval any scheme that bala...