arXiv research

Loss minimisation fails to capture epistemic uncertainty in second-order predictors.

In few-shot learning, typically, the loss function which is applied at test time is the one we are ultimately interested in minimising, such as the mean-squared-error loss for a regression problem. However, given that we have few samples at test time, we argue that the loss function that we are interested in minimising…

PINNs solve differential geometry problems in complex shapes.

A neural flow method minimizes Willmore energy for 2-surfaces in 3D space.

Denoising autoencoders (DAEs) are powerful deep learning models used for feature extraction, data generation and network pre-training. DAEs consist of an encoder and decoder which may be trained simultaneously to minimise a loss (function) between an input and the reconstruction of a corrupted version of the input. The…

Playlist recommendation involves producing a set of songs that a user might enjoy. We investigate this problem in three cold-start scenarios: (i) cold playlists, where we recommend songs to form new personalised playlists for an existing user; (ii) cold users, where we recommend songs to form new playlists for a new us…

The paper optimizes forecasting for risk-adjusted decisions under trading frictions.

Gradient flow with weight decay shows grokking effect in deep learning.

New findings show second-order scoring rules can't accurately represent epistemic uncertainty.

The paper studies properties of Sliced Wasserstein energy for discrete measures.

Study robust linear regression with outliers, providing exact asymptotics for ERM performance.

EVILL uses randomised perturbations to improve exploration in bandit problems.

GD converges in unstable regimes, even with oscillatory behavior.

In this paper we revisit the weighted likelihood bootstrap, a method that generates samples from an approximate Bayesian posterior of a parametric model. We show that the same method can be derived, without approximation, under a Bayesian nonparametric model with the parameter of interest defined as minimising an expec…

New algorithm reduces regret in stochastic bandit convex optimization.

Finding parameters that minimise a loss function is at the core of many machine learning methods. The Stochastic Gradient Descent algorithm is widely used and delivers state of the art results for many problems. Nonetheless, Stochastic Gradient Descent typically cannot find the global minimum, thus its empirical effect…

The study of a machine learning problem is in many ways is difficult to separate from the study of the loss function being used. One avenue of inquiry has been to look at these loss functions in terms of their properties as scoring rules via the proper-composite representation, in which predictions are mapped to probab…

Sharp stability result for maps near infinitely concentrated minimisers.

New results on hypersurfaces show no branch points, improving smoothness.

We study the problem of finding strain-minimising stream surfaces in a divergence-free vector field. These surfaces are generated by motions of seed curves that propagate through the field in a strain minimising manner, i.e., they move without stretching or shrinking, preserving the length of their arbitrary arc. In ge…

Let $Ω\subset \mathbb{R}^3$ be a Lipschitz domain, and consider a harmonic map $v: Ω\rightarrow \mathbb{S}^2$ with boundary data $v|\partialΩ= \varphi$ which minimises the Dirichlet energy. For $p\geq 2$, we show that any energy minimiser $u$ whose boundary map $ψ$ has a small $W^{1,p}$-distance to $\varphi$ is close t…

Wasserstein GANs fail to approximate Wasserstein distance, leading to their success.

We prove existence and regularity of minimisers for the Canham-Helfrich energy in the class of weak (possibly branched and bubbled) immersions of the $2$-sphere. This solves (the spherical case) of the minimisation problem proposed by Helfrich in 1973, modelling lipid bilayer membranes. On the way to prove the main res…

We study variational systems for space curves, for which the Lagrangian or action principle has a Euclidean symmetry, using the Rotation Minimising frame, also known as the Normal, Parallel or Bishop frame. Such systems have previously been studied using the Frenet-Serret frame. The Rotation Minimising frame has many a…

New method reduces cloud usage for mobile/IoT predictions.

Supervised learning requires the specification of a loss function to minimise. While the theory of admissible losses from both a computational and statistical perspective is well-developed, these offer a panoply of different choices. In practice, this choice is typically made in an \emph{ad hoc} manner. In hopes of mak…

We establish connectedness of volume constrained minimisers of energies involving surface tensions and convex potentials. By a previous result of McCann, this implies that minimisers are convex in dimension two. This positively answers an old question of Almgren. We also prove convexity of minimisers when the volume co…

Bayesian adversaries can outsmart traditional adversarial attacks.

Prevalidated ridge regression simplifies logistic regression for high-dimensional data.

Study optimizes Bitcoin futures hedging to reduce liquidation risk.

Study characterizes hulls and capacities on Riemannian manifolds, proving isoperimetric inequalities.

Mirror flow optimizes separable data problems, converging to a maximum margin classifier.

The study analyzes multi-class teacher-student perceptron performance and generalization errors.

In this paper, we develop a new aligned vertex convolutional network model to learn multi-scale local-level vertex features for graph classification. Our idea is to transform the graphs of arbitrary sizes into fixed-sized aligned vertex grid structures, and define a new vertex convolution operation by adopting a set of…

New bounds improve generalization in machine learning with high probability.

Characterizes harmonic morphisms preserving minimal submanifolds and finds novel area-minimising hypercones.

Optimal convex loss function improves regression coefficient estimation.

We study the Calabi functional on a ruled surface over a genus two curve. For polarisations which do not admit an extremal metric we describe the behaviour of a minimising sequence splitting the manifold into pieces. We also show that the Calabi flow starting from a metric with suitable symmetry gives such a minimising…

Proves strict inequality for minimizers of Willmore energy under isoperimetric constraints.

A new procedure is presented for the objective comparison and evaluation of default definitions. This allows the lender to find a default threshold at which the financial loss of a loan portfolio is minimised, in accordance with Basel II. Alternative delinquency measures, other than simply measuring payments in arrears…

New approach shapes error distribution in long-term forecasting.

Current approaches in approximate inference for Bayesian neural networks minimise the Kullback-Leibler divergence to approximate the true posterior over the weights. However, this approximation is without knowledge of the final application, and therefore cannot guarantee optimal predictions for a given task. To make mo…

In this paper, we formulate a method for minimising the expectation value of the procurement cost of electricity in two popular spot markets: {\it day-ahead} and {\it intra-day}, under the assumption that expectation value of unit prices and the distributions of prediction errors for the electricity demand traded in tw…

Deep neural networks are workhorse models in machine learning with multiple layers of non-linear functions composed in series. Their loss function is highly non-convex, yet empirically even gradient descent minimisation is sufficient to arrive at accurate and predictive models. It is hitherto unknown why are deep neura…

Approximate Bayesian computation (ABC) is a method for Bayesian inference when the likelihood is unavailable but simulating from the model is possible. However, many ABC algorithms require a large number of simulations, which can be costly. To reduce the computational cost, Bayesian optimisation (BO) and surrogate mode…

The Duffing oscillator's parameters are identified online using variational message passing.

We consider a one-period Kyle (1985) framework where the insider can be subject to a penalty if she trades. We establish existence and uniqueness of equilibrium for virtually any penalty function when noise is uniform. In equilibrium, the demand of the insider and the price functions are in general non-linear and remai…

The paper analyzes greedy algorithms for MMD minimization, showing their efficiency and approximation error.