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## Semi Superwised Algoritham Assignment Sample

### a) Convergence

Semi-supervised is the process to understand and determine the condition of future aspects depending upon the present variables. If it is described with examples, then it will be like there are two sentences 1first one is "Buy a house with money" and "buy a house with decoration". No, the mission is to determine what to select like a noun or preposition to fulfill the sentences.

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Fig 1: Semi-supervised

Fig 2: Semi-supervised

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### b) E step

Generative model for the semi-supervised the factors are like, maximize (X1, Y1, Xu/)

EM is the way to maximize it (Berthelot et al. 2019).

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### c) Semi supervised m step:

Let, ? be a set of N observed values Yj € IR^d. We define the joint density function,

Where ? stands for the parameters of the distribution, let us also suppose that ? is Gaussian Mixture with M modes, ,……,. For each mode K, K=1,….., M, we assume a Gaussian density conditional model (Iscen, et al. 2019),

This is parameterized by the mean and covariance of the mode. The unknown parameters of the observation model for all components are collectively denoted by

Where  = Prior probability of the model K.

We have to find Q of all observations with respect to the hidden variables X.

The ? set is divided into a labeled set s and an unlabelled set U, ?=S U U.

The general constraint for mode priors

In the supervised part, it is assumed that.

The ? function returns 1 if belongs to the mode or 0 otherwise. The maximization of ? results in the following semi-supervised update equations 1, 2, and 3, where the parameter t states for the iteration step (Oliver et al. 2018).

In these equations, the subset of supervised instances for a particular mode K is denoted as S (k). We have also simplified the notation in expression three, introducing

Therefore D will be a D= dimensional matrix. Update parameters µ, R, ? using the posteriors estimated in the E step in expressions 1, 2, and 3. The objective of the semi-supervised EM algorithm is to iteratively optimize the ? parameters (Park et al. 2017). The process stops when the change for the log-likelihood between two consecutive steps is less than certain ?. The threshold value used is set as ?=1/100 (1+D+ (D+1) D/2) log?? (ND) ?, where N is the number of samples, and D is the dimension of each sample.

### Lagrangian Equation for the semi-supervised Gaussian Mixture

#### f) Difference between semi-supervised and unsupervised EM

Within the semi-supervised EM, they got trained by the coding, and it should be labeled. The algorithm learns from the labeled data and process from that. It helps to predict those data which cannot be determined easily (Yang et al. 2016). Data science needs time to evaluate various data like scaling or building something in an accurate way.

Where the unsupervised EM is a machine learning technique where there is no need to supervise the program, here the machine will run without any label and no supervision is needed. The work goes on its own (Zhai et al. 2019). It has the capability to run more complex data. And due to this, the unsupervised data is more unpredictable.

#### JOURNAL:

Berthelot, D., Carlini, N., Goodfellow, I., Papernot, N., Oliver, A. and Raffel, C.A., 2019. Mixmatch: A holistic approach to semi-supervised learning. In Advances in Neural Information Processing Systems (pp. 5049-5059).

Iscen, A., Tolias, G., Avrithis, Y. and Chum, O., 2019. Label propagation for deep semi-supervised learning. In Proceedings of the IEEE conference on computer vision and pattern recognition (pp. 5070-5079).

Oliver, A., Odena, A., Raffel, C.A., Cubuk, E.D. and Goodfellow, I., 2018. Realistic evaluation of deep semi-supervised learning algorithms. In Advances in neural information processing systems (pp. 3235-3246).

Park, S., Park, J.K., Shin, S.J. and Moon, I.C., 2017. Adversarial dropout for supervised and semi-supervised learning. arXiv preprint arXiv:1707.03631.

Yang, Z., Cohen, W. and Salakhudinov, R., 2016, June. Revisiting semi-supervised learning with graph embeddings. In International conference on machine learning (pp. 40-48). PMLR.

Zhai, X., Oliver, A., Kolesnikov, A. and Beyer, L., 2019. S4l: Self-supervised semi-supervised learning. In Proceedings of the IEEE international conference on computer vision (pp. 1476-1485).

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