Density estimation

Résumé

In statistics, probability density estimation or simply density estimation is the construction of an estimate, based on observed data, of an unobservable underlying probability density function. The unobservable density function is thought of as the density according to which a large population is distributed; the data are usually thought of as a random sample from that population. A variety of approaches to density estimation are used, including Parzen windows and a range of data clustering techniques, including vector quantization. The most basic form of density estimation is a rescaled histogram. Example We will consider records of the incidence of diabetes. The following is quoted verbatim from the data set description: :A population of women who were at least 21 years old, of Pima Indian heritage and living near Phoenix, Arizona, was tested for diabetes mellitus according to World Health Organization criteria. The data were collected by the US National Insti

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https://en.wikipedia.org/wiki/Density_estimation

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Chargement

Density estimation with wavelets

Olivier Renaud

EPFL1999

Chargement

In this thesis, we present a data-driven iterative pipeline to generate, simulate and validate point-neuron models of the whole mouse brain. The ultimate goal is to replicate close loop experiments with a virtual body in a virtual world. This pipeline was origi-nally created by a PhD student of the Blue Brain Project and this pioneer work has yielded the first versions of the model and their simulations. My objective is to refine, extend and consolidate the previous version of the workflow and in particular to extend the repertoire of neuron types by integrating and consolidating available literature data.The pipeline has four main parts. First, we define a pair of reference atlases to create a spatial reference for every dataset that we want to integrate. Second, we create a cell atlas with estimates of the number and density of the major cell types in each brain region. Then, we build a connectivity atlas that describes the connections of each neuron of the mouse brain and their properties. Finally, we assign point-neuron parameters to each of the neuron types, and synaptic parameters to each of the connection types of our model to obtain a point-neuron network of the mouse brain. This network can be simulated to perform mouse brain experi-ments in-silico.In this thesis, we evaluate the quality of the different reference atlases, released by the Allen Institute for Brain Science and pro-vide methods to mitigate the impact of artifacts in the original images. We further extend the cell atlas with density estimates of more inhibitory neuron types. To do so, we introduce a new method to combine estimates of inhibitory neuron counts from the literature into a consistent framework. We also estimate inhibitory neuron density in regions where no literature data are avai-lable, using collected literature estimates and gene expression data from in situ hybridization image stacks. Our approach can be further extended to other cell types and provides a resource to build more detailed circuits of the mouse brain. Next, we refine the connectivity atlas, including literature findings on short-range connectivity. Additionally, we construct a database to store data collected on neuron types point-neuron parameters and synaptic parameters. With the results of the previous steps, we generate a new version of the whole mouse brain point-neuron network. We tested this new model against its previous version using three benchmark experiments. We explore the possibility to embed and connect detailed circuit reconstructions of the mouse brain to our point neuron model and co-simulate them. Finally, we constrain a 3D skeleton model of the mouse with joint constraints from the literature and attach muscle to its bones to create a musculoskeletal model of the mouse body that can be simulated in close-loop with our model to reproduce motor control experiments.

EPFL2022

Chargement

Population Sensing Using Mobile Devices

Farid Movahedi Naini

In our daily lives, our mobile phones sense our movements and interactions via a rich set of embedded sensors such as a GPS, Bluetooth, accelerometers, and microphones. This enables us to use mobile phones as agents for collecting spatio-temporal data. The idea of mining these spatio-temporal data is currently being explored for many applications, including environmental pollution monitoring, health care, and social networking. When used as sensing devices, a particular feature of mobile phones is their aspect of mobility, in contrast to static sensors. Furthermore, despite having useful applications, collecting data from mobile phones introduces privacy concerns, as the collected data might reveal sensitive information about the users, especially if the collector has access to auxiliary information. In the first part of this thesis, we use spatio-temporal data collected by mobile phones in order to evaluate different features of a population related to their mobility patterns. In particular, we consider the problems of population-size and population-density estimation that have applications, among others, in crowd monitoring, activity-hotspot detection, and urban analysis. We first conduct an experiment where ten attendees of an open-air music festival act as Bluetooth probes. Next, we construct parametric statistical models to estimate the total number of visible Bluetooth devices and their density in the festival area. We further test our proposed models against Wi-Fi traces obtained on the EPFL campus. We conclude that mobile phones can be effectively used as sensing devices to evaluate mobility-related parameters of a population. For the specific problem of population-density estimation, we investigate the mobility aspect of sensing: We quantitatively analyze the performance of mobile sensors compared to static sensors. Under an independent and identically distributed mobility model for the population, we derive the optimal random-movement strategy for mobile sensors in order to yield the best estimate of population density (in the mean-squared error sense). This enables us to plan an adaptive trajectory for the mobile sensors. In particular, we demonstrate that mobility brings an added value to the sensors; these sensors outperform static sensors for long observation intervals. In the second part of this thesis, we analyze the vulnerability of anonymized mobility statistics stored in the form of histograms. We consider an attacker who has access to an anonymized set of histograms of a set of users’ mobility traces and to an independent set of non-anonymized histograms of traces belonging to the same users. We study the hypothesis-testing problem of identifying the correct matching between the anonymized histograms and the non-anonymized histograms. We show that the solution can be obtained by using a minimum-weight matching algorithm on a complete weighted bipartite graph. By applying the algorithm to Wi-Fi traces obtained on the EPFL campus, we demonstrate that in fact anonymized histograms contain a significant amount of information that could be used to uniquely identify users by an attacker with access to auxiliary information about the users. Finally, we demonstrate how trust relationships between users can be exploited to enhance their privacy. We consider the specific problem of the privacy-preserving computation of functions of data that belong to users in a social network. An example of an application is a poll or a survey on a private issue. Most of the known non-cryptographic solutions to this problem can be viewed as belonging to one of the following two extreme regimes. The first regime is when every user trusts only herself and she is responsible for protecting her own privacy. In other words, the circle of trust of a user has a single member: herself. In the second regime, every user trusts herself and the server, but not any of the other users. In other words, the circle of trust of a user comprises herself and the server. We investigate this problem under the assumption that users are willing to share their private data with trusted friends in the network, hence we consider a regime in which the circle of trust of a user consists of herself and her friends. Thus, our approach falls in-between the two mentioned regimes. Our algorithm consists of first partitioning users into circles of trust and then computing the global function by using results of local computations within each circle. We demonstrate that such trust relationships can be exploited to significantly improve the tradeoff between the privacy of users' data and the accuracy of the computation.

EPFL2014

Chargement

Population Sensing Using Mobile Devices

Farid Movahedi Naini

EPFL2014

EPFL2022