A New Probabilistic Distance Metric With Application In Gaussian Mixture Reduction

This paper presents a new distance metric to compare two continuous probability density functions. The main advantage of this metric is that, unlike other statistical measurements, it can provide an analytic, closed-form expression for a mixture of Gaussian distributions while satisfying all metric properties. These characteristics enable fast, stable, and efficient calculations, which are highly desirable in real-world signal processing applications. The application in mind is Gaussian Mixture Reduction (GMR), which is widely used in density estimation, recursive tracking, and belief propagation. To address this problem, we developed a novel algorithm dubbed the Optimization-based Greedy GMR (OGGMR), which employs our metric as a criterion to approximate a high-order Gaussian mixture with a lower order. Experimental results show that the OGGMR algorithm is significantly faster and more efficient than state-of-the-art GMR algorithms while retaining the geometric shape of the original mixture

Real options theory and classification of patients by diagnosis related groups: how these different fields could relate?

Hospital organizations are inserted in a complex environment, which makes decision-making a challenge for managers. Therefore, tools and techniques, which seek to understand the past and project the future, are commonly used. In some situations, the observed complexity requires the transfer of knowledge from other areas, in order to find solutions and develop tools that provide an efficient management of resources, integrating what has been done with future projections. In this scenario, this article aims to present a theoretical discussion on the Theory of Real Options - ROT and the Diagnosis Related Groups - DRG, both used in the hospital environment, but for different purposes. Through a bibliographic search, this discussion is justified by the existing gap in the subject and by trying to show how ROT and DRG are related and can be used in a complementary way. The results show that both are applied in the hospital environment with the objective of supporting decision making, taking into account the patient's condition in their analysis in a relevant way. However, ROT and DRG have differences that make the junction of their concepts relevant to decision making.In a complex environment, the managers of hospital organizations should take hard decisions all the time. Therefore, tools and techniques, which seek to understand the past and project the future, are very important. In some situations, the complexity encountered requires the transfer of knowledge from other areas, to find solutions and develop tools that provide efficient management of resources. In this scenario, this article has the main objective to present a theoretical discussion that brings the relationship between the Theory of Real Options and the Diagnosis Related Groups, to identify possible points that underlie the use of real options in Diagnosis Related Groups. The results demonstrate that, with the patient’s condition as the focus, both are applied in the hospital environment with the objective of supporting decision-making, but not together. In addition, the differences observed make the combination of some of its concepts relevant for decision-making

DataDAM: Efficient Dataset Distillation with Attention Matching

Researchers have long tried to minimize training costs in deep learning while maintaining strong generalization across diverse datasets. Emerging research on dataset distillation aims to reduce training costs by creating a small synthetic set that contains the information of a larger real dataset and ultimately achieves test accuracy equivalent to a model trained on the whole dataset. Unfortunately, the synthetic data generated by previous methods are not guaranteed to distribute and discriminate as well as the original training data, and they incur significant computational costs. Despite promising results, there still exists a significant performance gap between models trained on condensed synthetic sets and those trained on the whole dataset. In this paper, we address these challenges using efficient Dataset Distillation with Attention Matching (DataDAM), achieving state-of-the-art performance while reducing training costs. Specifically, we learn synthetic images by matching the spatial attention maps of real and synthetic data generated by different layers within a family of randomly initialized neural networks. Our method outperforms the prior methods on several datasets, including CIFAR10/100, TinyImageNet, ImageNet-1K, and subsets of ImageNet-1K across most of the settings, and achieves improvements of up to 6.5% and 4.1% on CIFAR100 and ImageNet-1K, respectively. We also show that our high-quality distilled images have practical benefits for downstream applications, such as continual learning and neural architecture search.Comment: Accepted in International Conference in Computer Vision (ICCV) 202

Statics and dynamics of pulp fibres

grantor: University of TorontoFlexible pulp fibres produce paper of higher quality than their stiff counterparts. The pulp and paper industry has a keen interest to measure fibre flexibility and to fractionate fibres based on flexibility. The objective of this thesis is to theoretically study the static and dynamic behaviour of pulp fibres with direct applications to fibre flexibility measurement devices and fibre screening. Governing equations, which represent the deflection and motion of pulp fibres, are developed and numerical methods are utilized to solve the mathematical formulations. Static large deflection beam theory is applied to the geometry of four existing fibre flexibility measurement devices to determine the advantages and shortcomings of each method. It is shown that the small deflection analysis predicts flexibility with an error of less than 10% when compared to the large deflection analysis for fibre deflections of less than 20% of the span length. Furthermore, it is concluded that a better estimate of the hydrodynamic forces acting on the pulp fibres is required. To study the behaviour of flexible fibres in pulp screening applications, non-linear equations representing the motion of a flexible fibre are developed. Two methods to represent the dynamic interaction of a fibre with the flow domain walls are proposed. Together with a Computational Fluid Dynamics (CFD) analysis, the motion of fibres in a channel flow with a slot are studied and the effect of fibre flexibility on the ability of the fibres to pass through the slot is examined. For the first time, a theoretical model has been used to show that screening based on fibre flexibility does occur. However, it is shown that the predominant property which governs the fractionation of fibres is the fibre length. To propose a direct method to model the flow of a flexible fibre for future applications and a method to predict the hydrodynamic forces acting on a fibre, an automatic three-dimensional finite element mesh generating algorithm, based on the Delaunay triangulation, is developed for use with CFD software. A unique method of mesh refinement is defined and it is shown that the method is extremely efficient for typical fibre geometries.Ph.D

A Closed-Form Model for Valuing Real Options Using Managerial Cash-Flow Estimates- Draft Abstract for ROC2013 ∗

In this work, we build on a previous real options approach that utilizes managerial cash-flow estimates to value early stage project investments. Through a simplifying assumption, where we assume that the managerial cash-flow estimates are normally distributed, we derive a closedform solution to the real option problem. The model is developed through the introduction of a market sector indicator, which is assumed to be correlated to a tradeable market index, which drives the project’s sales estimates. Another indicator, assumed partially correlated to the sales indicator drives the gross margin percent estimates. In this way we can model a cash-flow process that is partially correlated to a traded market index. This provides the mechanism for valuing real options of the cash-flow in a financially consistent manner under the risk-neutral minimum martingale measure. The method requires minimal subjective input of model parameters and is very easy to implement. We also investigate the sensitivity of the normal distribution assumption by comparing the approach developed here to our previous approach