Doubly Stochastic Variational Inference for Deep Gaussian Processes

Gaussian processes (GPs) are a good choice for function approximation as they are flexible, robust to over-fitting, and provide well-calibrated predictive uncertainty. Deep Gaussian processes (DGPs) are multi-layer generalisations of GPs, but inference in these models has proved challenging. Existing approaches to inference in DGP models assume approximate posteriors that force independence between the layers, and do not work well in practice. We present a doubly stochastic variational inference algorithm, which does not force independence between layers. With our method of inference we demonstrate that a DGP model can be used effectively on data ranging in size from hundreds to a billion points. We provide strong empirical evidence that our inference scheme for DGPs works well in practice in both classification and regression.Comment: NIPS 201

Un progetto di storia condivisa: un’ipotesi di guida alla storia contemporanea di una regione transfrontaliera

Subito dopo la Seconda guerra mondiale l’UNESCO aveva invitato gli Stati aderenti a promuovere commissioni miste internazionali di storici per affrontare insieme i nodi conflittuali del passato. Ma è stata solo la fine della Guerra Fredda a imprime¬re una decisa accelerazione a tale impostazione degli studi. Un siffatto indirizzo metodologico e storiografico è venuto affermandosi su larga scala anche in Italia: l’Istituto storico italo-germanico in Trento è riuscito a superare le antistoriche barriere esistenti, riscoprendo, e rivalutando, l’eredità d’un inestimabile patrimonio comune “mit¬teleuropeo”. Queste sommarie note su quanto si va facendo per una storia condivisa su quello che era il nostro confine orientale servono da introduzione al progetto av¬viato due anni orsono dal Centro interdipartimentale di ricerca sulla pace “Ire¬ne” dell’Università degli Studi di Udine, che prevede la collaborazione di altri atenei per la stesura d’una guida comune transfrontaliera per insegnanti delle scuole secondarie superiori sulla storia contemporanea dell’area alto-adriatica dal 1848 al 2007

Escuela y comunidad. Participación comunitaria en el sistema escolar.

This article is based mainly on the results of a project to which the author is participating. INCLUD-ED Project, �Strategies for inclusion and social cohesion in Europe from education� (2006-2011; http://creaub.info/included/), is an Integrated Project of the priority 7, �Citizens and governance in the knowledge-based society� of the 6th Framework Programme of the European Commission. The main objective of the INCLUD-ED integrated project is to analyse educational strategies that contribute to social inclusion and cohesion and educational strategies that lead to social exclusion, in the context of the European knowledge based society, providing key elements and action lines to improve educational and social policy. The Coordinator of the Project are the University of Barcelona and CREA (Centre de Recerca Social i Educativa, http://www.pcb.ub.edu/homepcb/live/ct/p576.asp) and the Department of Education of the University of Florence (http://www.sciedu.unifi.it/mdswitch.html) is part of the partnership.Este artículo se basa en los resultados de un proyecto en el que la autora participa. INCLUD-ED Project, �Strategies for inclusion and social cohesion in Europe from education� (2006-2011; http://creaub.info/included/), es un Proyecto Integrado Prioridad 7 �Citizens and governance in the knowledge-based society� de VI Programa Marco de la Comisión Europea. El objetivo principal del proyecto INCLUD-ED es analizar las estrategias educativas que contribuyan a la cohesión e inclusión social y las estrategias de educación que conducen a la exclusión social, en una iniciativa en contra de la exclusión social, proporcionando los elementos clave y pautas de actuación para mejorar la formación política y social. El coordinador del proyecto es la Universidad de Barcelona, junto con el CREA (Centre de Recerca Social i Educativa, http://www.pcb.ub.edu/homepcb/live/ct/p576.asp) y El Departamento de Educación de la Universidad de Florencia (http://www.sciedu.unifi.it/mdswitch.html) que forma parte del consorcio de investigación

David Lewis : la vie d'un philosophe

Une biographie intellectuelle du philosophe David Lewis

Orthogonally Decoupled Variational Gaussian Processes

Gaussian processes (GPs) provide a powerful non-parametric framework for reasoning over functions. Despite appealing theory, its superlinear computational and memory complexities have presented a long-standing challenge. State-of-the-art sparse variational inference methods trade modeling accuracy against complexity. However, the complexities of these methods still scale superlinearly in the number of basis functions, implying that that sparse GP methods are able to learn from large datasets only when a small model is used. Recently, a decoupled approach was proposed that removes the unnecessary coupling between the complexities of modeling the mean and the covariance functions of a GP. It achieves a linear complexity in the number of mean parameters, so an expressive posterior mean function can be modeled. While promising, this approach suffers from optimization difficulties due to ill-conditioning and non-convexity. In this work, we propose an alternative decoupled parametrization. It adopts an orthogonal basis in the mean function to model the residues that cannot be learned by the standard coupled approach. Therefore, our method extends, rather than replaces, the coupled approach to achieve strictly better performance. This construction admits a straightforward natural gradient update rule, so the structure of the information manifold that is lost during decoupling can be leveraged to speed up learning. Empirically, our algorithm demonstrates significantly faster convergence in multiple experiments.Comment: Appearing NIPS 201

Deep Gaussian Processes: Advances in Models and Inference

Hierarchical models are certainly in fashion these days. It seems difficult to navigate the field of machine learning without encountering `deep' models of one sort or another. The popularity of the deep learning revolution has been driven by some striking empirical successes, prompting both intense rapture and intense criticism. The criticisms often centre around the lack of model uncertainty, leading to sometimes drastically overconfident predictions. Others point to the lack of a mechanism for incorporating prior knowledge, and the reliance on large datasets. A widely held hope is that a Bayesian approach might overcome these problems. The deep Gaussian process presents a paradigm for building deep models from a Bayesian perspective. A Gaussian process is a prior for functions. A deep Gaussian process uses several Gaussian process functions and combines them hierarchically through composition (that is, the output of one is the input to the next). The deep Gaussian process promises to capture the compositional nature of deep learning while mitigating some of the disadvantages through a Bayesian approach. The thesis develops deep Gaussian process modelling in a number of ways. The model is first interpreted differently from previous work, not as a `hierarchical prior' but as a factorized prior with an hierarchical likelihood. Mean functions are suggested to avoid issues of degeneracy and to aid initialization. The main contribution is a new method of inference that avoids the burden of representing the function values directly through an application of sparse variational inference. This method scales to arbitrarily large data and is shown to work well in practice through experiments. The use of variational inference recasts (approximate) inference as optimization of Gaussian distributions. This optimization has an exploitable geometry via the natural gradient. The natural gradient is shown to be advantageous for single layer non-conjugate models, and for the (final layer of a) deep Gaussian process model. Deep Gaussian processes can be a model both for complex associations between variables and complex marginal distributions of single variables. Incorporating noise in the hierarchy leads to complex marginal distribution through the non-linearities of the mappings at each layer. The inference required for noisy variables cannot be handled with sparse methods, as sparse methods rely on correlations between variables, which are absent for noisy variables. Instead, a more direct approach is developed, using an importance weighted variational scheme.Open Acces

Relación entre el talento humano, las competencias laborales y la rentabilidad en la pyme argentina

The prime objective of this project was to know the main competences of the human resources of Small and Medium Enterprises (SMEs) focused in service, and their relationship with the productivity of the company. A qualitative and exploratory methodology was used, through the technique of in-depth interviews. The unit of analysis was services SMEs in Buenos Aires City and Great Buenos Aires. 82 in-depth interviews were conducted during the second half of 2016. It could be observed there was coincidence, on the part of the interviewees, that the training of the personnel is limited to the application of specific activities. In general, there was no interest in comprehensive training, but rather in the basic knowledge to work in their assigned roles. The companies are oriented to the training in the position rather than to comprehensive training. Staff acknowledges the good working environment, the proximity to the management, the flexibility of activities, and the relationship between members of the company as determining factors in the development of the human resources within the company. Only in 1 out of 10 cases there exists a HR department, and the selection and recruitment is generally done by the owners themselves. The level of studies of the staff is not as valued as the experience or knowledge in their role. In 8 out of 10 cases, high school education predominates as the highest level of studies reached by both middle and high management, and there is no evidence of an interest in continuous training in the workplace. Skill is considered to be achieved through practice and experience in the position, not through formal training. SME managers have also expressed that they do not receive the incentive, resources, or sufficient support from the Government to carry out their activities, developing and evolving in their target market. Only 1 out of 5 employees responds to have had formal training during the past three years. The lack of budget is the most frequent response (8 out of 10) to justify it. Only 3 out of 10 managers say that training affects the profitability of their company, adding that it is only possible to see improvements in the medium term. However, faced with the question of the importance of human talent in the profitability of the company, more than 7 out of 10 recognize that it is quite or very important. This reflects a certain contradiction. The new questions that arise for possible future research are whether highly trained personnel could be backed up by SMEs, and if the benefit - cost ratio would justify this.El objetivo de este proyecto fue conocer las competencias principales del personal de las pymes de servicio, y su relación con la productividad en ellas. Se utilizó una metodología cualitativa y exploratoria mediante la técnica de entrevistas en profundidad. Como unidad de análisis se seleccionaron pymes de servicio en CABA y GBA. Fueron realizadas 82 entrevistas en profundidad durante el segundo semestre de 2016. Pudo observarse la coincidencia, por parte de los entrevistados, en que la formación del personal se encuentra acotada a la aplicación de actividades específicas. No se observó, en general, un interés por una formación integral, sino por un conocimiento básico para desenvolverse en el rol correspondiente. Las empresas se orientan a la capacitación en el puesto más que a una formación integral. El personal reconoce en el buen clima laboral, la cercanía con la dirección, la flexibilidad de actividades, y el vínculo entre los integrantes de la empresa como factores determinantes en el cuanto al desarrollo del recurso humano dentro de esta. Solo en 1 de cada 10 casos existe un departamento de RRHH, y la selección y reclutamiento son en general realizados por los mismos dueños. El nivel de estudio del personal no es tan valorado como sí lo es la experiencia o conocimiento en el rol a desempeñar. En 8 de cada 10 de los casos predomina el colegio secundario como máximo nivel de estudios alcanzado tanto por los mandos medios como por la dirección, y no se evidencia un interés por una capacitación continua en el puesto de trabajo. Se considera que la pericia es lograda con la práctica y la experiencia en el puesto, y no a través de una capacitación formal. Los directivos de las pymes han expresado también que no reciben, por parte del Estado, el incentivo, los recursos, ni el apoyo suficiente para llevar adelante sus actividades; con lo cual se desarrollan y evolucionan en su mercado meta. Solo 1 de cada 5 empleados responde haber recibido capacitación formal durante los últimos tres años. La falta de presupuesto es la respuesta de mayor frecuencia (8 de cada 10) para justificar su carencia. Solo 3 de cada 10 directivos afirman que la capacitación incide en la rentabilidad de su empresa, y agregan que solo es posible ver mejoras en el mediano plazo. Sin embargo, frente a la pregunta de cuál es la importancia del talento humano en la rentabilidad de la empresa, más de 7 de cada 10 reconoce que es medianamente o muy importante. Esto refleja cierta contradicción. Las nuevas preguntas que surgen para una futura posible investigación son si el personal altamente formado y capacitado podría ser solventado por las pymes, y si la relación beneficio–costo lo justificaría