arXiv subjects

Huong Ha

Publications and source records attributed to Huong Ha.

25 records · Page 2Linked to original sources

arXiv2020

High Dimensional Level Set Estimation with Bayesian Neural Network

Level Set Estimation (LSE) is an important problem with applications in various fields such as material design, biotechnology, machine operational testing, etc. Existing techniques suffer from the scalability issue, that is, these methods do not work well with high dimensional inputs. This paper proposes novel methods to solve the high dimensional LSE problems using Bayesian Neural Networks. In particular, we consider two types of LSE problems: (1) \textit{explicit} LSE problem where the threshold level is a fixed user-specified value, and, (2) \textit{implicit} LSE problem where the threshold level is defined as a percentage of the (unknown) maximum of the objective function. For each problem, we derive the corresponding theoretic information based acquisition function to sample the data points so as to maximally increase the level set accuracy. Furthermore, we also analyse the theoretical time complexity of our proposed acquisition functions, and suggest a practical methodology to efficiently tune the network hyper-parameters to achieve high model accuracy. Numerical experiments on both synthetic and real-world datasets show that our proposed method can achieve better results compared to existing state-of-the-art approaches.

stat.ML↗

arXiv2020

Sub-linear Regret Bounds for Bayesian Optimisation in Unknown Search Spaces

Bayesian optimisation is a popular method for efficient optimisation of expensive black-box functions. Traditionally, BO assumes that the search space is known. However, in many problems, this assumption does not hold. To this end, we propose a novel BO algorithm which expands (and shifts) the search space over iterations based on controlling the expansion rate thought a hyperharmonic series. Further, we propose another variant of our algorithm that scales to high dimensions. We show theoretically that for both our algorithms, the cumulative regret grows at sub-linear rates. Our experiments with synthetic and real-world optimisation tasks demonstrate the superiority of our algorithms over the current state-of-the-art methods for Bayesian optimisation in unknown search space.

stat.ML↗

arXiv2020

Distributionally Robust Bayesian Quadrature Optimization

Bayesian quadrature optimization (BQO) maximizes the expectation of an expensive black-box integrand taken over a known probability distribution. In this work, we study BQO under distributional uncertainty in which the underlying probability distribution is unknown except for a limited set of its i.i.d. samples. A standard BQO approach maximizes the Monte Carlo estimate of the true expected objective given the fixed sample set. Though Monte Carlo estimate is unbiased, it has high variance given a small set of samples; thus can result in a spurious objective function. We adopt the distributionally robust optimization perspective to this problem by maximizing the expected objective under the most adversarial distribution. In particular, we propose a novel posterior sampling based algorithm, namely distributionally robust BQO (DRBQO) for this purpose. We demonstrate the empirical effectiveness of our proposed framework in synthetic and real-world problems, and characterize its theoretical convergence via Bayesian regret.

cs.LG↗

arXiv2019

Bayesian Optimization with Unknown Search Space

Applying Bayesian optimization in problems wherein the search space is unknown is challenging. To address this problem, we propose a systematic volume expansion strategy for the Bayesian optimization. We devise a strategy to guarantee that in iterative expansions of the search space, our method can find a point whose function value within epsilon of the objective function maximum. Without the need to specify any parameters, our algorithm automatically triggers a minimal expansion required iteratively. We derive analytic expressions for when to trigger the expansion and by how much to expand. We also provide theoretical analysis to show that our method achieves epsilon-accuracy after a finite number of iterations. We demonstrate our method on both benchmark test functions and machine learning hyper-parameter tuning tasks and demonstrate that our method outperforms baselines.

stat.ML↗

arXiv2018

An analysis of the SPARSEVA estimate for the finite sample data case

In this paper, we develop an upper bound for the SPARSEVA (SPARSe Estimation based on a VAlidation criterion) estimation error in a general scheme, i.e., when the cost function is strongly convex and the regularized norm is decomposable for a pair of subspaces. We show how this general bound can be applied to a sparse regression problem to obtain an upper bound for the traditional SPARSEVA problem. Numerical results are used to illustrate the effectiveness of the suggested bound.

math.ST↗

arXiv2017

Useful redundancy in parameter and time delay estimation for continuous-time models

This paper proposes an algorithm to estimate the parameters, including time delay, of continuous time systems based on instrumental variable identification methods. To overcome the multiple local minima of the cost function associated with the estimation of a time delay system, we utilise the useful redundancy technique. Specifically, the cost function is filtered through a set of low-pass filters to improve convexity with the useful redundancy technique exploited to achieve convergence to the global minimum of the optimization problem. Numerical examples are presented to demonstrate the effectiveness of the proposed algorithm.

math.ST↗

arXiv2015

Reweighted nuclear norm regularization: A SPARSEVA approach

The aim of this paper is to develop a method to estimate high order FIR and ARX models using least squares with re-weighted nuclear norm regularization. Typically, the choice of the tuning parameter in the reweighting scheme is computationally expensive, hence we propose the use of the SPARSEVA (SPARSe Estimation based on a VAlidation criterion) framework to overcome this problem. Furthermore, we suggest the use of the prediction error criterion (PEC) to select the tuning parameter in the SPARSEVA algorithm. Numerical examples demonstrate the veracity of this method which has close ties with the traditional technique of cross validation, but using much less computations.

math.OC↗