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Stochastic differential equations can describe a wide range of dynamical systems, and obtaining the governing equations of these systems is the premise of studying the nonlinear dynamic behavior of the system. Neural networks are currently…
In NMT we search for the mode of the model distribution to form predictions. The mode and other high-probability translations found by beam search have been shown to often be inadequate in a number of ways. This prevents improving…
We propose a method for program generation based on semantic scaffolds, lightweight structures representing the high-level semantic and syntactic composition of a program. By first searching over plausible scaffolds then using these as…
Bayesian synthetic likelihood (BSL) is a popular method for estimating the parameter posterior distribution for complex statistical models and stochastic processes that possess a computationally intractable likelihood function. Instead of…
Selection functions are vital for understanding the observational biases of spectroscopic surveys. With the wide variety of multi-object spectrographs currently in operation and becoming available soon, we require easily generalisable…
In this paper we present a novel quasi-Newton algorithm for use in stochastic optimisation. Quasi-Newton methods have had an enormous impact on deterministic optimisation problems because they afford rapid convergence and computationally…
In many contemporary optimization problems such as those arising in machine learning, it can be computationally challenging or even infeasible to evaluate an entire function or its derivatives. This motivates the use of stochastic…
We consider a variant of the stochastic gradient descent (SGD) with a random learning rate and reveal its convergence properties. SGD is a widely used stochastic optimization algorithm in machine learning, especially deep learning. Numerous…
For modelling geophysical systems, large-scale processes are described through a set of coarse-grained dynamical equations while small-scale processes are represented via parameterizations. This work proposes a method for identifying the…
Decoding sits between a language model and everything we do with it, yet it is still treated as a heuristic knob-tuning exercise. We argue decoding should be understood as a principled optimisation layer: at each token, we solve a…
Building upon our earlier work of a martingale approach to global optimization, a powerful stochastic search scheme for the global optimum of cost functions is proposed on the basis of change of measures on the states that evolve as…
Optimized sensing is important for computational imaging in low-resource environments, when images must be recovered from severely limited measurements. In this paper, we propose a physics-constrained, fully differentiable, autoencoder that…
Validating and controlling safety-critical systems in uncertain environments necessitates probabilistic reachable sets of future state evolutions. The existing methods of computing probabilistic reachable sets normally assume that…
Sparse signal recovery from a small number of random measurements is a well known NP-hard to solve combinatorial optimization problem, with important applications in signal and image processing. The standard approach to the sparse signal…
The problem of sequentially maximizing the expectation of a function seeks to maximize the expected value of a function of interest without having direct control on its features. Instead, the distribution of such features depends on a given…
Finding an optimal decision tree that minimizes classification error is known to be NP-hard. While exact algorithms based on MILP, CP, SAT, or dynamic programming guarantee optimality, they often suffer from poor anytime behavior -- meaning…
Stochastic gradient descent method and its variants constitute the core optimization algorithms that achieve good convergence rates for solving machine learning problems. These rates are obtained especially when these algorithms are…
The partial monitoring (PM) framework provides a theoretical formulation of sequential learning problems with incomplete feedback. On each round, a learning agent plays an action while the environment simultaneously chooses an outcome. The…
The process of dynamic state estimation (filtering) based on point process observations is in general intractable. Numerical sampling techniques are often practically useful, but lead to limited conceptual insight about optimal…
Boson sampling devices are a prime candidate for exhibiting quantum supremacy, yet their application for solving problems of practical interest is less well understood. Here we show that Gaussian boson sampling (GBS) can be used for dense…