Paper uses machine learning in EM framework for better nowcasting.
problem Improving risk estimation with incomplete information.
method Expectation-maximisation framework with machine learning for occurrence and reporting modeling.
result XGBoost-based approach outperforms existing methods in nowcasting.
The mutual information is a core statistical quantity that has applications in all areas of machine learning, whether this is in training of density models over multiple data modalities, in maximising the efficiency of noisy transmission channels, or when learning behaviour policies for exploration by artificial agents…
We consider expected utility maximisation problem for exponential Levy models and HARA utilities in presence of illiquid asset in portfolio. This illiquid asset is modelled by an option of European type on another risky asset which is correlated with the first one. Under some hypothesis on Levy processes, we give the e…
For information retrieval and binary classification, we show that precision at the top (or precision at k) and recall at the top (or recall at k) are maximised by thresholding the posterior probability of the positive class. This finding is a consequence of a result on constrained minimisation of the cost-sensitive exp…
Bayesian active learning method improved for censored regression data.
problem Challenges in estimating BALD for censored regression data.
method Derived entropy and mutual information for censored distributions, developed C-BALD objective, proposed novel modelling approach. result Demonstrated C-BALD outperforms other methods in censored regression. New Variational InfoMax objective improves neural network performance.
problem Optimizing neural networks using Bayesian Inference and Information Bottleneck.
method Derive Variational InfoMax (VIM) objective that maximizes InfoMax directly.
result VIM improves model performance in accuracy, robustness, and representation quality.
Implicit stochastic models, where the data-generation distribution is intractable but sampling is possible, are ubiquitous in the natural sciences. The models typically have free parameters that need to be inferred from data collected in scientific experiments. A fundamental question is how to design the experiments so…
Learning disentangled representation from any unlabelled data is a non-trivial problem. In this paper we propose Information Maximising Autoencoder (InfoAE) where the encoder learns powerful disentangled representation through maximizing the mutual information between the representation and given information in an unsu…
Researchers tackle insider trading in incomplete markets using a discrete-time jump process approach.
problem Tackles insider trading in incomplete markets under the trinomial model.
method Uses a marked binomial process and stochastic analysis with Malliavin calculus.
result Identifies insider expected additional utility with Shannon entropy of extra information.
New method extracts cosmological information from dark matter halo catalogues using graph neural networks.
problem Quantifying cosmological information from large-scale structure data.
method Implicit likelihood approach with Information Maximising Neural Networks (IMNNs) on graph representations of dark matter halo catalogues.
result Graph neural network summaries can extract information from noisy catalogues and improve parameter constraints.
We propose a projection pursuit (PP) algorithm based on Gaussian mixture models (GMMs). The negentropy obtained from a multivariate density estimated by GMMs is adopted as the PP index to be maximised. For a fixed dimension of the projection subspace, the GMM-based density estimation is projected onto that subspace, wh…
Framework for multi-scale clustering using phase transitions.
problem Clustering datasets with multi-scale structures.
method Cascade of phase transitions in simulated annealing of Expectation-Maximisation algorithm with weighted local covariance.
result Approximation of the number and size of clusters at different scales.
We show that the Reeb vector, and hence in particular the volume, of a Sasaki-Einstein metric on the base of a toric Calabi-Yau cone of complex dimension n may be computed by minimising a function Z on R^n which depends only on the toric data that defines the singularity. In this way one can extract certain geometric i…
New neural network approach using mutual information.
problem Training neural networks for imbalanced datasets.
method Converts neural network classifiers to mutual information evaluators.
result New form of softmax leads to better classification accuracy, especially for imbalanced datasets.
We propose a method to learn causal response representations through direct effect analysis.
problem Uncovering direct causal effects in complex, multivariate settings.
method Our method bridges conditional independence testing with causal representation learning, formulating an optimisation problem to maximise evidence against conditional independence.
result The largest eigenvalue distribution can be bounded by an F-distribution, providing testable conditional independence. This paper explores optimising acquisition functions in Bayesian optimisation.
problem Optimising acquisition functions in Bayesian optimisation is challenging due to their non-convex nature.
method The authors derive compositional forms for acquisition functions and use them to recast maximisation as a compositional optimisation problem.
result The compositional approach to maximising acquisition functions shows empirical advantages across various tasks.
DHOG improves unsupervised clustering accuracy on image benchmarks.
problem Local optima in mutual information maximisation lead to suboptimal representations.
method Deep hierarchical object grouping (DHOG) computes multiple discrete representations in a hierarchical order.
result DHOG achieves new state-of-the-art results on three main benchmarks.
Improves inference from sparse data with hybrid summary statistics.
problem Robust simulation-based inference from limited data.
method Augment traditional summary statistics with neural network outputs to maximize mutual information.
result Improves information extraction and makes inference robust in low-data settings.
Proposes EPIG for active learning to improve predictive performance.
problem Suboptimal predictive performance of traditional active learning methods.
method Introduces EPIG, a new acquisition function measuring information gain in the space of predictions.
result EPIG leads to stronger predictive performance compared to BALD across various datasets and models.
A simple strategy optimizes broker-client trading, reducing price discounts for informed traders.
problem Optimizing broker-client trading to balance client flow and informed trader losses.
method Modelled as a stochastic control problem, derived optimal strategy in closed form, introduced algorithm.
result Optimal strategy reduces price discounts for informed traders, balancing client flow and informed trader losses.
We study the problem of causal discovery through targeted interventions. Starting from few observational measurements, we follow a Bayesian active learning approach to perform those experiments which, in expectation with respect to the current model, are maximally informative about the underlying causal structure. Unli…
Paper derives second variation formula for eigenvalue functionals on surfaces.
problem Determine if a critical metric is a local maximizer for eigenvalue functionals.
method Derive second variation formula for critical metrics and apply to specific cases.
result Flat metric on non-rhombic torus cannot be a conformal maximizer for first eigenvalue.
Two deep learning algorithms solve utility maximisation problems in finance.
problem Solving utility maximisation problems in finance with deep learning.
method Two algorithms: one for Markovian problems via HJB equation and 2BSDE, the other for non-Markovian problems via adjoint BSDE.
result Highly accurate results with low computational cost, solving problems with power, log, and non-HARA utilities in various models.
We consider utility maximization problem for semi-martingale models depending on a random factor ξ. We reduce initial maximization problem to the conditional one, given ξ=u, which we solve using dual approach. For HARA utilities we consider information quantities like Kullback-Leibler information and Hellinger inte…
New constraints rule out some optimal domains for helicity maximisation.
problem Finding a smooth domain of fixed volume that maximizes helicity.
method Established additional geometric constraints on optimal domains.
result Ruled out the optimality of a broad class of solid tori.
We derive expressions for the predicitive information rate (PIR) for the class of autoregressive Gaussian processes AR(N), both in terms of the prediction coefficients and in terms of the power spectral density. The latter result suggests a duality between the PIR and the multi-information rate for processes with mutua…
In this paper we formulate the nonnegative matrix factorisation (NMF) problem as a maximum likelihood estimation problem for hidden Markov models and propose online expectation-maximisation (EM) algorithms to estimate the NMF and the other unknown static parameters. We also propose a sequential Monte Carlo approximatio…
Study Nash equilibrium between broker and trader in a lit exchange with price impact.
problem Optimizing trading strategies between informed and uninformed traders with broker's inventory penalties.
method Characterized Nash equilibrium through FBSDEs, solved explicitly.
result Explicit solution to trading strategies of broker and informed trader.
We study the existence and properties of metrics maximising the first Laplace eigenvalue among conformal metrics of unit volume on Riemannian surfaces. We describe a general approach to this problem and its higher eigenvalue versions via the direct method of calculus of variations. The principal results include the gen…
Mutual information is widely applied to learn latent representations of observations, whilst its implication in classification neural networks remain to be better explained. We show that optimising the parameters of classification neural networks with softmax cross-entropy is equivalent to maximising the mutual informa…
SSLfmm package improves semi-supervised learning by incorporating informative missingness in finite mixture models.
problem Improving semi-supervised learning with informative missingness in datasets.
method Estimates Bayes' classifier under a finite mixture model with MCAR and MAR missingness mechanisms.
result The classifier trained on partially labelled data can achieve lower misclassification rates than supervised methods.
Paper develops duality theory for robust utility maximization in continuous time.
problem Maximizing utility in the presence of uncertainty.
method Introduces a duality theory for continuous-time robust utility maximization problems.
result Shows duality between robust utility maximization and a conjugate problem under certain conditions.
The study proves properties of optimizers for sets maximizing perimeter under fixed volume constraints.
problem Existence and properties of bounded convex sets in Riemannian manifolds maximizing perimeter under fixed volume constraints.
method Analyzes the properties of optimizers for sets maximizing perimeter under fixed volume constraints in Euclidean, spherical, and hyperbolic spaces.
result Proves that there are no C2-maximisers of perimeter with prescribed volume and that the smallest principal curvature is constant in regions where the set is of class C2. Optimizes fund manager's wealth with partial information on market risk.
problem Maximizing wealth with incomplete information about market risk.
method Formulated as optimization under partial information, solved via martingale method and concavification.
result Shows how learning about market risk affects optimal investment strategy.
In financial markets valuable information is rarely circulated homogeneously, because of time required for information to spread. However, advances in communication technology means that the 'lifetime' of important information is typically short. Hence, viewed as a tradable asset, information shares the characteristics…
The paper addresses optimal control in modern tontines with bequest preferences, showing a linear investment strategy.
problem Optimal controls and decreasing allocation in modern tontines with bequest preferences.
method Dual approach to solve optimal control problems with power utilities, modeling bequest preferences.
result Investment strategy almost linearly adjusts from 0% to 100% over time.
Introduces relative information gain for improving Gaussian process regression rates.
problem Improving the sample complexity of estimating or maximizing unknown functions.
method Introduces relative information gain, interpolates between effective dimension and information gain, and proves PAC-Bayesian bounds.
result Obtains minimax-optimal rates of convergence through the relative information gain.
While the channel capacity reflects a theoretical upper bound on the achievable information transmission rate in the limit of infinitely many bits, it does not characterise the information transfer of a given encoding routine with finitely many bits. In this note, we characterise the quality of a code (i. e. a given en…
Despite great popularity of applying softmax to map the non-normalised outputs of a neural network to a probability distribution over predicting classes, this normalised exponential transformation still seems to be artificial. A theoretic framework that incorporates softmax as an intrinsic component is still lacking. I…
Study optimal reinsurance pricing under model uncertainty for multiple insurers.
problem Optimal reinsurance pricing in the presence of multiple sources of model uncertainty.
method Solves a continuous-time Stackelberg game for general reinsurance contracts, considering entropy penalties and ambiguity in insurers' models.
result Reinsurer prices under a distortion of the barycentre of insurers' models, maximizing expected wealth with an entropy penalty.
The notion of utility maximising entropy (u-entropy) of a probability density, which was introduced and studied by Slomczynski and Zastawniak (Ann. Prob 32 (2004) 2261-2285, arXiv:math.PR/0410115 v1), is extended in two directions. First, the relative u-entropy of two probability measures in arbitrary probability space…
Study eigenvalues of magnetic Steklov problem on Riemannian annuli.
problem Eigenvalues of magnetic Steklov problem on Riemannian annuli.
method Sharp upper bounds, maximizers, and existence of maximizers for eigenvalues.
result Existence of maximizers for the second normalized eigenvalue for rotationally invariant metrics.
Study optimizes trading strategies in markets with transaction costs and uncertain models.
problem Optimizing trading strategies in markets with transaction costs and model uncertainty.
method Maximizing worst-case expected utility over a class of models on a filtered probability space.
result Existence of optimal trading strategies for general càdlàg price processes and incomplete filtrations.
Optimizes experimental designs for intractable models using mutual information bounds.
problem Finding optimal experimental designs for models with intractable data-generating distributions.
method Maximizes mutual information lower bounds parametrized by neural networks, updating network parameters and designs simultaneously.
result Framework enables experimental design for various tasks including parameter estimation and model discrimination.
This article is devoted to the maximisation of HARA utilities of L{é}vy switching process on finite time interval via dual method. We give the description of all f-divergence minimal martingale measures in initially enlarged filtration, the expression of their Radon-Nikodym densities involving Hellinger and Kulback-Lei…
Agent maximizes utility with pathwise constraint on portfolio value.
problem Maximizing utility with a pathwise constraint on portfolio value.
method Max-plus decomposition for supermartingales, Black-Scholes-Merton model.
result Explicit form of optimal terminal wealth and process involved.
This paper introduces GEMINI, a new mutual information metric for unsupervised neural network training.
problem The mutual information (MI) as a clustering objective does not lead to satisfactory clusters.
method The authors generalised MI by changing its core distance, introducing GEMINIs that do not require regularizations and can automatically select the number of clusters.
result GEMINIs can automatically select the number of clusters without requiring a priori knowledge of the number of clusters.
Paper compares hard and soft EM for BN learning from incomplete data.
problem Learning BNs from incomplete data using EM algorithms.
method Investigates the impact of imputation vs. belief propagation in hard and soft EM.
result A decision tree can guide practitioners in choosing the best EM algorithm.