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"Brahmaputra Degree College, established in 1993, is a general degree college situated at Bokulguri, in Lakhimpur district, Assam. This college is affiliated with the Dibrugarh University. Department=Arts *Assamese *English *History *Physical Education *Economics *Philosophy *Political Science *Geography ReferencesExternal links *http://www.brahmaputradegreecollege.edu.in/ Category:Universities and colleges in Assam Category:Colleges affiliated to Dibrugarh University Category:Educational institutions established in 1993 Category:1993 establishments in India "
"In probability theory, statistics, and machine learning, the continuous Bernoulli distributionLoaiza-Ganem, G., & Cunningham, J. P. (2019). The continuous Bernoulli: fixing a pervasive error in variational autoencoders. In Advances in Neural Information Processing Systems (pp. 13266-13276).PyTorch Distributions. https://pytorch.org/docs/stable/distributions.html#continuousbernoulliTensorflow Probability. https://www.tensorflow.org/probability/api_docs/python/tfp/edward2/ContinuousBernoulli is a family of continuous probability distributions parameterized by a single shape parameter \lambda \in (0, 1), defined on the unit interval x \in [0, 1], by: : p(x \lambda) \propto \lambda^x (1-\lambda)^{1-x}. The continuous Bernoulli distribution arises in deep learning and computer vision, specifically in the context of variational autoencoders,Kingma, D. P., & Welling, M. (2013). Auto-encoding variational bayes. arXiv preprint arXiv:1312.6114.Kingma, D. P., & Welling, M. (2014, April). Stochastic gradient VB and the variational auto-encoder. In Second International Conference on Learning Representations, ICLR (Vol. 19). for modeling the pixel intensities of natural images. As such, it defines a proper probabilistic counterpart for the commonly used binary cross entropy loss, which is often applied to continuous, [0,1]-valued data.Larsen, A. B. L., Sønderby, S. K., Larochelle, H., & Winther, O. (2016, June). Autoencoding beyond pixels using a learned similarity metric. In International conference on machine learning (pp. 1558-1566).Jiang, Z., Zheng, Y., Tan, H., Tang, B., & Zhou, H. (2017, August). Variational deep embedding: an unsupervised and generative approach to clustering. In Proceedings of the 26th International Joint Conference on Artificial Intelligence (pp. 1965-1972).PyTorch VAE tutorial: https://github.com/pytorch/examples/tree/master/vae.Keras VAE tutorial: https://blog.keras.io/building-autoencoders-in-keras.html. This practice amounts to ignoring the normalizing constant of the continuous Bernoulli distribution, since the binary cross entropy loss only defines a true log- likelihood for discrete, {0,1}-valued data. The continuous Bernoulli also defines an exponential family of distributions. Writing \eta = \log\left(\lambda/(1-\lambda)\right) for the natural parameter, the density can be rewritten in canonical form: p(x \eta) \propto \exp (\eta x) . Related distributions = Bernoulli distribution The continuous Bernoulli can be thought of as a continuous relaxation of the Bernoulli distribution, which is defined on the discrete set {0,1} by the probability mass function: : p(x) = p^x (1-p)^{1-x}, where p is a scalar parameter between 0 and 1. Applying this same functional form on the continuous interval [0,1] results in the continuous Bernoulli probability density function, up to a normalizing constant. Beta distribution The Beta distribution has the density function: : p(x) \propto x^{\alpha - 1} (1-x)^{\beta - 1}, which can be re-written as: : p(x) \propto x_1^{\alpha_1 - 1} x_2^{\alpha_2 - 1}, where \alpha_1, \alpha_2 are positive scalar parameters, and (x_1, x_2) represents an arbitrary point inside the 1-simplex, \Delta^{1} = { (x_1, x_2): x_1 > 0, x_2 > 0, x_1 + x_2 = 1 } . Switching the role of the parameter and the argument in this density function, we obtain: : p(x) \propto \alpha_1^{x_1} \alpha_2^{x_2}. This family is only identifiable up to the linear constraint \alpha_1 + \alpha_2 = 1 , whence we obtain: : p(x) \propto \lambda^{x_1} (1-\lambda)^{x_2}, corresponding exactly to the continuous Bernoulli density. Exponential distribution An exponential distribution restricted to the unit interval is equivalent to a continuous Bernoulli distribution with appropriate parameter. Continuous categorical distribution The multivariate generalization of the continuous Bernoulli is called the continuous categorical.Gordon-Rodriguez, E., Loaiza- Ganem, G., & Cunningham, J. P. (2020). The continuous categorical: a novel simplex-valued exponential family. In 36th International Conference on Machine Learning, ICML 2020. International Machine Learning Society (IMLS). References Category:Continuous distributions Category:Exponential family distributions "
"Swahid Maniram Dewan College, established in 1964, is a general degree college situated at Charing, in Sivasagar district, Assam. This college is affiliated with the Dibrugarh University. Departments=Arts *Assamese *English *History *Economics *Philosophy *Political Science *Geography ReferencesExternal links Category:Universities and colleges in Assam Category:Colleges affiliated to Dibrugarh University Category:Educational institutions established in 1964 Category:1964 establishments in India "