In the design of support vector machines an important step is to select the optimal hyperparameters. One of the most used estimators of the performance is the Radius-Margin bound. Some modifications of this bound have been made to adapt it to soft margin problems, giving a convex optimization problem for the L2 soft margin formulation. However, it is still interesting to consider the L1 case du...

In this paper, we study a proximal-like algorithm for minimizing a closed proper function f(x) subject to x ≥ 0, based on the iterative scheme: x ∈ argmin{f(x)+ μkd(x, x k−1)}, where d(·, ·) is an entropy-like distance function. The algorithm is welldefined under the assumption that the problem has a nonempty and bounded solution set. If, in addition, f is a differentiable quasi-convex function...

Abstract. The inverse first passage time problem asks whether, for a Brownian motion B and a nonnegative random variable ζ, there exists a timevarying barrier b such that P{Bs > b(s), 0 ≤ s ≤ t} = P{ζ > t}. We study a “smoothed” version of this problem and ask whether there is a “barrier” b such that E[exp(−λ ∫ t 0 ψ(Bs − b(s)) ds)] = P{ζ > t}, where λ is a killing rate parameter and ψ : R → [0...

Complex computer simulators are increasingly used across fields of science as generative models tying parameters of an underlying theory to experimental observations. Inference in this setup is often difficult, as simulators rarely admit a tractable density or likelihood function. We introduce Adversarial Variational Optimization (AVO), a likelihood-free inference algorithm for fitting a non-di...

We introduce a new model, the Recurrent Entity Network (EntNet). It is equipped with a dynamic long-term memory which allows it to maintain and update a representation of the state of the world as it receives new data. For language understanding tasks, it can reason on-the-fly as it reads text, not just when it is required to answer a question or respond as is the case for a Memory Network (Suk...

In this paper we consider the minimization of a continuous function that is potentially not differentiable or not twice differentiable on the boundary of the feasible region. By exploiting an interior point technique, we present firstand second-order optimality conditions for this problem that reduces to classical ones when the derivative on the boundary is available. For this type of problems,...

In this paper, we use the Riemann-Liouville fractionalintegrals to establish some new integral inequalities related toChebyshev's functional in the case of two differentiable functions.

In this paper we show that the optimal exercise boundary/ free boundary of the American put option pricing problem for jump diffusions is continuously differentiable (except at the maturity). We also discuss the higher order regularity of the free boundary.

We discuss an approach for the problem of morphing two simple differentiable closed curves composed of quadric arcs maintaining both topology and differentiability in-between. Our approach makes use of a field of directions defined on triangulations.