In professional 3D animation artists model movements and scenes using rig functions - constrained set of sliders or controllers that propagate deformations and drive mechanism of object or character in systems of 3D tools. These controllers are manually built for each character and cannot be reused if the underlying structure is not exactly the same. There are often hundreds of adjustable parameters, and artists have to learn the structure for each new character. This is usually bottleneck in production, that might be avoided by automating this process. D. Holden et. al. proposed possible solutions using Gaussian Processes Regression, which showed useful in the case of skeletal (quadriped) characters. We want to further apply this on face model, that has a completely different structure than the skeletal model. In this work we explain the model for 3D face animation, the theory of Gaussian processes regression and a method to apply it for solving the problem of interest. At the end results and examples are presented with a simple animation model we have at our disposal.
We know too well that the effective operation of a queueing system requires maintaining the traffic intensity at a target value. This important measure of congestion can be monitored by using control charts, such as the one found in the seminal work by Bhat and Rao (1972) or more recently in Chen and Zhou (2015). For all intents and purposes, this paper focus on three control statistics chosen by Morais and Pacheco (2016) for their simplicity, recursive and Markovian character:
the number of customers left behind in the M/G/1 system by the n-th departing customer;
the number of customers seen in the GI/M/1 system by the n-th arriving customer;
the waiting time of the n-th arriving customer to the GI/G/1 system.
Since an upward and a downward shift in the traffic intensity are associated with a deterioration and an improvement (respectively) of the quality of service, the timely detection of these changes is an imperative requirement, hence, begging for the use of ARL-unbiased charts Pignatiello et al. (1995), in the sense that they detect any shifts in the traffic intensity sooner than they trigger a false alarm. In this paper, we focus on the design of these type of charts for the traffic intensity of the three single server queues mentioned above.
In this talk we address, in the context of real options, an investment problem with two sources of uncertainty: the price (reflected in the revenue of the firm) and the level of technology. The level of technology impacts in the investment cost, that decreases when there is a technology innovation. The price follows a geometric Brownian motion, whereas the technology innovations are driven by a Poisson process. As a consequence, the investment region may be attained in a continuous way (due to an increase of the price) or in a discontinuous way (due to a sudden decrease of the investment cost).
For this optimal stopping problem no analytical solution is known, and therefore we propose a quasi-analytical method to find an approximated solution that preserves the qualitative features of the exact solution. This method is based on a truncation procedure and we prove that the truncated solution converges to the solution of the original problem.
We provide results for the comparative statics for the investment thresholds. These results show interesting behaviors, particularly, the investment may be postponed or anticipated with the intensity of the technology innovations and with their impact on the investment cost.
(joint work with Carlos Oliveira and Rita Pimentel)
In this talk we will look at the optimal control problem of a firm that may operate in two different modes, one being more risky than the other, in the sense that in case the demand decreases, the return of the risky mode is lower than with the more conservative mode. On the other side, in case the demand increases, the opposite holds. The switches between these two alternative modes have associated costs. In both modes, there is the option to exit the market.
We will focus on two different parameter scenarios, that describe particular (and somehow extreme) economic situations. In the first scenario, we assume that the market is expected to increase in such a way that once the firm is producing in the more risky mode, it is never optimal to switch to the more conservative one. In the second scenario, there is a hysteresis region, where the firm is waiting in the more risky mode, in production, until some drop or increase in the demand leads to an exit or changing to the more conservative mode. This hysteresis region cannot be attained under continuous production.
We then address the problem of the optimal time to invest under each situation. Depending on the relation between the switching costs (equal or different from one mode to another), it may happen that the firm invests in the hysteresis region.
Joint work with Cláudia Nunes and Carlos Oliveira.
Feature selection problems arise in a variety of applications, such as microarray analysis, clinical prediction, text categorization, image classification and face recognition, multi-label learning, and classification of internet traffic. Among the various classes of methods, forward feature selection methods based on mutual information have become very popular and are widely used in practice. However, comparative evaluations of these methods have been limited by being based on specific datasets and classifiers. In this talk, we discuss a theoretical framework that allows evaluating the methods based on their theoretical properties. The estimation difficulties of the method’s objective functions will also be addressed.
This is a joint work with Francisco Macedo, António Pacheco, and Rui Valadas.
Much work has been done recently to make neural networks more interpretable, and one obvious approach is to arrange for the network to use only a subset of the available features. In linear models, Lasso (or $\ell_1$-regularized) regression assigns zero weights to the most irrelevant or redundant features, and is widely used in data science. However the Lasso only applies to linear models. Here we introduce LassoNet, a neural network framework with global feature selection. Our approach enforces a hierarchy: specifically a feature can participate in a hidden unit only if its linear representative is active. Unlike other approaches to feature selection for neural nets, our method uses a modified objective function with constraints, and so integrates feature selection with the parameter learning directly. As a result, it delivers an entire regularization path of solutions with a range of feature sparsity. On systematic experiments, LassoNet significantly outperforms state-of-the-art methods for feature selection and regression. The LassoNet method uses projected proximal gradient descent, and generalizes directly to deep networks. It can be implemented by adding just a few lines of code to a standard neural network.
In this talk, I will discuss a geometric interpretation to Bayesian inference that will yield a natural measure of the level of agreement between priors, likelihoods, and posteriors. The starting point for the construction of the proposed geometry is the observation that the marginal likelihood can be regarded as an inner product between the prior and the likelihood. A key concept in our geometry is that of compatibility, a measure which is based on the same construction principles as Pearson correlation, but which can be used to assess how much the prior agrees with the likelihood, to gauge the sensitivity of the posterior to the prior, and to quantify the coherency of the opinions of two experts. Estimators for all the quantities involved in our geometric setup are discussed, which can be directly computed from the posterior simulation output. Some examples are used to illustrate our methods, including data related to on-the-job drug usage, midge wing length, and prostate cancer.
The current COVID-19 pandemic is putting an enormous pressure not just in the society but also in all the scientific community.
If we want to follow a scientific approach to respond to the doubts and challenges that were generated, we need to find a balance between the most robust data, the best experimental methodologies to address the new problems and all the uncertainty associated.
In this presentation we will try to address this balance between best available data, clinical research methodology and uncertainty applied to what we know about pandemics, vaccine development and clinical trials. There will be a particular focus on the COVID-19 pandemic data and current research efforts for the development of vaccines and efficacious treatments.
Droughts, high temperatures and strong winds are key causes of the recent bushfires that have touched a major part of the Australian territory. Such extreme events seem to appear with increasing frequency, creating an urgent need to better understand the behaviour of extreme environmental phenomena. Max-stable processes are a widely popular tool to model spatial extreme events with several flexible models available in the literature. For inference on max-stable models, exact likelihood estimation becomes quickly computationally intractable as the number of spatial locations grows, limiting their applicability to large study regions or fine grids. In this talk, we introduce two methodologies based on composite likelihoods, to circumvent this issue. First, we assume the occurrence times of maxima available in order to incorporate the Stephenson-Tawn concept into the composite likelihood framework. Second, we propose to aggregate the information between locations into histograms and to derive a composite likelihood variation for these summaries. The significant improvements in performance of each estimation procedures is established through simulation studies and illustrated on two temperature datasets from Australia.
The area under the ROC curve (AUC) is the most commonly used index in the ROC methodology to evaluate the performance of a classifier that discriminates between two mutually exclusive conditions. The AUC can admit values between 0.5 and 1, where values close to 1 indicate that the model of classification has a high discriminative power. The overlap coefficient (OVL) between two density functions is defined as the common area between both functions. This coefficient is used as a measure of agreement between two distributions presenting values between 0 and 1, where values close to 1 reveal total overlapping densities. These two measures were used to construct the arrow plot to select differential expressed genes. A simulation study using the bootstrap method is presented in order to estimate AUC bias and standard error using empirical and kernel methods. In order to assess the impact of the OVL variation on the AUC bias, samples from various distributions were simulated considering different values for its parameters and for fixed OVL values between 0 and 1. Samples of dimensions 15, 30, 50 and 100 and 1000 bootstrap replicates for each scenario were considered.
We consider stochastic processes arising from chaotic systems by evaluating an heavy tailed observable function along the orbits of the system. We prove the convergence of a normalised sum process to a Lévy process with excursions, designed to describe the oscillations observed during the clusters of extremal observations. The applications to specific systems include both hyperbolic and non-uniformly expanding systems.
State-space models (SSMs) are a popular tool for modeling animal abundances. Inference difficulties for simple linear SSMs are well known, particularly in relation to simultaneous estimation of process and observation variances. Here we identify improvements for inference about nonlinear stage-structured SSMs fit with biased sequential life stage data using both theoretical and simulation-based assessments. The model is applied to modelling the life cycle of an endangered fish, Delta Smelt, which has been the focus of much political and legal controversy. This talk includes the historical and political background that motivated the statistical work and discusses the centrality of statistical methodology to guiding and justifying management actions aimed at protecting the fish.
Random missing data can constitute a problem when modelling rare events. Imputation is crucial in these situations and therefore models that describe different imputation functions enhance possible applications and enlarge the few known families of models which cover these situations. In this talk, we consider a family of models $\{Y_n\}, n\geq 1$, that can be associated to automatic systems which have a periodic control, in the sense that it is guaranteed that at instants multiple of $T$, $T\geq 2$, no value is lost. Random missing values are here replaced by the biggest of the previous observations up to the one surely registered.
We characterize the extremal behaviour of $\{Y_n\}, n\geq 1$, and obtain its extremal index expression. A consistent estimator for the model parameter is also proposed and its finite sample behaviour analysed.
Joint work with Helena Ferreira (UBI) and Maria da Graça Temido (UC).
The prevalence of cooperation among human societies is a puzzle that has caught the eye of researchers from multiple fields. Why is that people are selfless and often incur costs to aid others? Theoretical and experimental works have shown that status and reputations can provide solutions to the cooperation conundrum. These elements are often framed in the context of indirect reciprocity, which constitutes one of the most elaborate mechanisms of cooperation discovered so far. By helping someone, individuals may increase their reputation, which can change the predisposition of others to help them in the future. The reputation of an individual depends, in turn, on the social norms that establish what characterizes a good or bad action. Such norms are often so complex that an individual’s ability to follow subjective rules becomes important. Here I will present a mathematical framework — grounded on game theory and stochastic birth-death processes — capable of identifying the key pattern of the norms that promote cooperation, and those that do so at a minimum complexity. This combination of high cooperation and low complexity suggests that simple moral principles, and informal institutions based on reputations, can elicit cooperation even in complex environments.
This is a joint work with Fernando P. Santos (Princeton University) and Jorge M. Pacheco (Universidade do Minho).
In observational longitudinal studies it is common to have repeated measures of more than one process that changes over time, being the main objective understanding the association between the two processes and if there is a more relevant one. For example, in a weekly psychotherapy process several evaluations are made to the client as symptomatology, empathy to the psychoterapist or proportion of innovative moments. In these studies it is important to understand in which way symptomatology and innovative moments are associated and to identify which process drives individual changes. In this talk we propose a multivariate model for two longitudinal variables in the context of linear mixed models, exploring different correlation structures in such a way to be possible to answer to the scientific questions. Different distributions will be discussed for longitudinal variables.
Quantile regression relies on minimizing the conditional quantile loss, which is based on the quantile check function. This has been extended to flexible regression functions such as the quantile regression forest (Meinshausen, 2006) and the gradient forest (Athey et al., 2019). These methods break down if the quantile of interest lies outside of the range of the data. Extreme value theory provides the mathematical foundation for estimation of such extreme quantiles. A common approach is to approximate the exceedances over a high threshold by the generalized Pareto distribution. For conditional extreme quantiles, one may model the parameters of this distribution as functions of the predictors. Up to now, the existing methods are either not flexible enough (e.g., linear methods) or do not generalize well in higher dimensions (e.g., kernel based methods). We develop a new approach based on gradient boosting for extreme quantile regression that estimates the parameters of the generalized Pareto distribution in a flexible way even in higher dimensions. We discuss cross-validation of the tuning parameters and show how the importance of the different predictors can be measured. Our estimator outperforms classical quantile regression methods and methods from extreme value theory in simulations studies. We study an application to forecasting of extreme precipitation in statistical post-processing.
This is joint work with Jasper Velthoen, Clement Dombry and Juan-Juan Cai.
Joint modelling to analyse longitudinal and survival data in the presence of competing risks has received much attention in the recent years and it is becoming increasingly used in clinical studies. The many well-established models proposed to analyse separately longitudinal and time-to-event outcomes are not suitable when the longitudinal outcome and survival endpoints are associated. Although some joint models were adapted in order to allow for competing endpoints, this methodology has not been widely disseminated and used in clinical research.
In this seminar, joint modelling of longitudinal and survival data in a competing risk context is presented, discussing the different parameterizations of systematic implementations of these models in the R statistical software. To demonstrate the relevance of these models in clinical research, an example on peritoneal dialysis is considered.
