6,067 research outputs found
A sparse multinomial probit model for classification
A recent development in penalized probit modelling using a hierarchical Bayesian approach has led to a sparse binomial (two-class) probit classifier that can be trained via an EM algorithm. A key advantage of the formulation is that no tuning of hyperparameters relating to the penalty is needed thus simplifying the model selection process. The resulting model demonstrates excellent classification performance and a high degree of sparsity when used as a kernel machine. It is, however, restricted to the binary classification problem and can only be used in the multinomial situation via a one-against-all or one-against-many strategy. To overcome this, we apply the idea to the multinomial probit model. This leads to a direct multi-classification approach and is shown to give a sparse solution with accuracy and sparsity comparable with the current state-of-the-art. Comparative numerical benchmark examples are used to demonstrate the method
Hybrid approximate message passing
Gaussian and quadratic approximations of message passing algorithms on graphs have attracted considerable recent attention due to their computational simplicity, analytic tractability, and wide applicability in optimization and statistical inference problems. This paper presents a systematic framework for incorporating such approximate message passing (AMP) methods in general graphical models. The key concept is a partition of dependencies of a general graphical model into strong and weak edges, with the weak edges representing interactions through aggregates of small, linearizable couplings of variables. AMP approximations based on the Central Limit Theorem can be readily applied to aggregates of many weak edges and integrated with standard message passing updates on the strong edges. The resulting algorithm, which we call hybrid generalized approximate message passing (HyGAMP), can yield significantly simpler implementations of sum-product and max-sum loopy belief propagation. By varying the partition of strong and weak edges, a performance--complexity trade-off can be achieved. Group sparsity and multinomial logistic regression problems are studied as examples of the proposed methodology.The work of S. Rangan was supported in part by the National Science Foundation under Grants 1116589, 1302336, and 1547332, and in part by the industrial affiliates of NYU WIRELESS. The work of A. K. Fletcher was supported in part by the National Science Foundation under Grants 1254204 and 1738286 and in part by the Office of Naval Research under Grant N00014-15-1-2677. The work of V. K. Goyal was supported in part by the National Science Foundation under Grant 1422034. The work of E. Byrne and P. Schniter was supported in part by the National Science Foundation under Grant CCF-1527162. (1116589 - National Science Foundation; 1302336 - National Science Foundation; 1547332 - National Science Foundation; 1254204 - National Science Foundation; 1738286 - National Science Foundation; 1422034 - National Science Foundation; CCF-1527162 - National Science Foundation; NYU WIRELESS; N00014-15-1-2677 - Office of Naval Research
Complementarity in the innovation strategy: Internal R&D, external technology acquisition, and cooperation in R&D.
Successful innovation depends on the development and integration of new knowledge in the innovation process. In order to successfully innovate, the firm will combine different innovation activities. In addition to doing own research and development, firms typically are engaged in the acquisition of knowledge on the technology market and cooperate actively in R&D with other firms and research organizations. In this paper we show that there exist important complementarities between the different innovation activities. We test complementarity between the innovation activities both directly, through the productivity approach, and indirectly, through the adoption approach. Using data from the Community Innovation Survey on Belgian manufacturing firms, we show that firms that are only engaged in a single innovation strategy, either internal R&D activities or sourcing technology externally, introduced fewer new and substantially improved products compared to firms which combine internal and external sourcing. This result is consistent with complementarity between own R&D and external technology sourcing activities. In the adoption approach we show that the different innovation activities are strongly positively correlated and identify common drivers, resulting in the perceived complementarity between these innovation activities. An important finding is that a more basic R&D base which may serve as an absorptive capacity and a capacity to strategically protect intellectual property are important common drivers for the different innovation activitiesManagement; Innovation strategy
Discriminative conditional restricted Boltzmann machine for discrete choice and latent variable modelling
Conventional methods of estimating latent behaviour generally use attitudinal
questions which are subjective and these survey questions may not always be
available. We hypothesize that an alternative approach can be used for latent
variable estimation through an undirected graphical models. For instance,
non-parametric artificial neural networks. In this study, we explore the use of
generative non-parametric modelling methods to estimate latent variables from
prior choice distribution without the conventional use of measurement
indicators. A restricted Boltzmann machine is used to represent latent
behaviour factors by analyzing the relationship information between the
observed choices and explanatory variables. The algorithm is adapted for latent
behaviour analysis in discrete choice scenario and we use a graphical approach
to evaluate and understand the semantic meaning from estimated parameter vector
values. We illustrate our methodology on a financial instrument choice dataset
and perform statistical analysis on parameter sensitivity and stability. Our
findings show that through non-parametric statistical tests, we can extract
useful latent information on the behaviour of latent constructs through machine
learning methods and present strong and significant influence on the choice
process. Furthermore, our modelling framework shows robustness in input
variability through sampling and validation
Estimating the joint distribution of independent categorical variables via model selection
Assume one observes independent categorical variables or, equivalently, one
observes the corresponding multinomial variables. Estimating the distribution
of the observed sequence amounts to estimating the expectation of the
multinomial sequence. A new estimator for this mean is proposed that is
nonparametric, non-asymptotic and implementable even for large sequences. It is
a penalized least-squares estimator based on wavelets, with a penalization term
inspired by papers of Birg\'{e} and Massart. The estimator is proved to satisfy
an oracle inequality and to be adaptive in the minimax sense over a class of
Besov bodies. The method is embedded in a general framework which allows us to
recover also an existing method for segmentation. Beyond theoretical results, a
simulation study is reported and an application on real data is provided.Comment: Published in at http://dx.doi.org/10.3150/08-BEJ155 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
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