A Cluster Elastic Net for Multivariate Regression

We propose a method for estimating coefficients in multivariate regression when there is a clustering structure to the response variables. The proposed method includes a fusion penalty, to shrink the difference in fitted values from responses in the same cluster, and an L1 penalty for simultaneous variable selection and estimation. The method can be used when the grouping structure of the response variables is known or unknown. When the clustering structure is unknown the method will simultaneously estimate the clusters of the response and the regression coefficients. Theoretical results are presented for the penalized least squares case, including asymptotic results allowing for p >> n. We extend our method to the setting where the responses are binomial variables. We propose a coordinate descent algorithm for both the normal and binomial likelihood, which can easily be extended to other generalized linear model (GLM) settings. Simulations and data examples from business operations and genomics are presented to show the merits of both the least squares and binomial methods.Comment: 37 Pages, 11 Figure

Collective Uncertainty in Partially-Polarized and Partially-Decohered Spin-1/2 Systems

It has become common practice to model large spin ensembles as an effective pseudospin with total angular momentum J = N x j, where j is the spin per particle. Such approaches (at least implicitly) restrict the quantum state of the ensemble to the so-called symmetric Hilbert space. Here, we argue that symmetric states are not generally well-preserved under the type of decoherence typical of experiments involving large clouds of atoms or ions. In particular, symmetric states are rapidly degraded under models of decoherence that act identically but locally on the different members of the ensemble. Using an approach [Phys. Rev. A 78, 052101 (2008)] that is not limited to the symmetric Hilbert space, we explore potential pitfalls in the design and interpretation of experiments on spin-squeezing and collective atomic phenomena when the properties of the symmetric states are extended to systems where they do not apply.Comment: 13 pages, 7 figure

The David Thompson Memorial Fort: An Early Outpost of Historically Themed Tourism in Western Canada

The David Thompson Memorial Fort was western Canada’s first purpose-built historically themed tourist attraction. Constructed in Invermere, BritishColumbia, in 1922, it was part of a larger campaign by a politically connectedland development company to establish a tourist trade that would spur economicgrowth in an underdeveloped region. The Memorial Fort was sponsored by theCanadian Pacific Railway and Hudson’s Bay Company and was novel not only forusing the past to draw tourists in a region where sublime mountain scenery was thestaple attraction, but also for being intended to draw automobile-borne tourists toa region where railways had traditionally been the dominant mode of conveyance.Plans to make the Memorial Fort into a tourist-oriented museum faltered due tothe collapse of the land company that had pushed for it. Nevertheless, the fact thatit was built with support from powerful backers illustrates the growing enthusiasmfor both historically themed tourism and the automobile as a way of experiencingit in Canada during the early interwar years.Le fort commémoratif David-Thompson est la première attraction touristiquede l’Ouest du Canada à avoir été érigée expressément en fonction d’un thèmehistorique. Construit à Invermere (Colombie-Britannique) en 1922, le fortfaisait partie d’une vaste campagne menée par une société d’aménagementdes terres ayant des contacts politiques dans le but de mettre en place uneindustrie touristique qui stimulerait la croissance économique dans une régionsous-développée. Commandité par le Chemin de fer Canadien Pacifique et laCompagnie de la Baie d’Hudson, le fort commémoratif était une nouveauté parcequ’il utilisait le passé pour attirer des touristes dans une région où la beautédes paysages de montagne constituait la principale attraction, et en plus, parcequ’il visait à attirer des touristes voyageant en automobile dans une région où lechemin de fer avait été jusque-là le mode de transport dominant. Les plans visantà transformer le fort commémoratif en musée ont fait long feu en raison de lafaillite de la société immobilière qui les avait mis de l’avant. Néanmoins, le faitque le fort ait été construit avec l’appui de puissants commanditaires témoigne de l’enthousiasme grandissant tant pour le tourisme à caractère historique quepour l’automobile comme moyen de s’y adonner au Canada au début de l’entre-deux-guerres

Study of young infants as social beings

In theories of development, an important but controversial question is whether or not young infants are social beings. For example, it is often argued that, while infants may appear to interact with adults, this is a mistaken impression until such a time as they have fulfilled certain theoretically defined criteria for sociability. The aims of this study were first, empirically to evaluate arguments for and against the view that infants have an EtXel,i sensitivity to other persons, and secondly, if such a sensitivity were found, to discover how it develops during the first six months of life. Both an experiment and detailed naturalistic observations were made to answer the first question. The experiment produced preliminary evidence that the behaviour of two- month -olds is consistently different with persons and with graspable objects. This finding was supported by fine -grain analysis of a filmed interaction between a two -month -old and her mother which produced conclusive evidence that young infants are sensitive not only to the form of others' actions but to the social significance of their actions, insofar as those actions affect the infant's immediate interests. Subsequent observations and experiments were made to find how social sensitivity or 'intersubjectivity' develops during the first six months of life. These involved comparisons between infants' behaviour when interacting with their mother, with strangers and with novel and familiar face -masks. Behaviour was recorded on video-tape for approximately four minutes in each condition, twice a month, between six and twenty -eight weeks of age. Findings showed that there is a peak of social interest between six and ten weeks of age which is followed by a decline. This decline was due to a general increase in infants' ability to take active control of their surroundings - typified by their increased interest in objects and in playing interpersonal games (as opposed to participating in 'conversational' adult-infant exchanges). Associated with this decline of interest was increased 'negativity' during interactions with the mother and with other stimuli (i.e. actions of refusing or shutting out contact with other entities). Twelve examples of negativity are described in detail. The thesis also includes a theoretical contribution to Lacan's and Winnicott's notion of 'mirroring', based on the analysis of maternal babytalk. This suggests that mirroring is not simply a social phenomenon but is also an ideological phenomenon and constitutes, therefore, a complex and salient form of social influence during early infancy. The thesis concludes with a Spinozan argument that, notwithstanding their innate sensitivity to other persons, the development of infants as persons should be viewed as a more all- embracing process than is usually connoted by the phrase 'social development'; namely, as just one expression of the essential process by which humans increase their power of self - determination

On the Use of Minimum Penalties in Statistical Learning

Modern multivariate machine learning and statistical methodologies estimate parameters of interest while leveraging prior knowledge of the association between outcome variables. The methods that do allow for estimation of relationships do so typically through an error covariance matrix in multivariate regression which does not scale to other types of models. In this article we proposed the MinPEN framework to simultaneously estimate regression coefficients associated with the multivariate regression model and the relationships between outcome variables using mild assumptions. The MinPen framework utilizes a novel penalty based on the minimum function to exploit detected relationships between responses. An iterative algorithm that generalizes current state of the art methods is proposed as a solution to the non-convex optimization that is required to obtain estimates. Theoretical results such as high dimensional convergence rates, model selection consistency, and a framework for post selection inference are provided. We extend the proposed MinPen framework to other exponential family loss functions, with a specific focus on multiple binomial responses. Tuning parameter selection is also addressed. Finally, simulations and two data examples are presented to show the finite sample properties of this framewok