**I-Optimality**

The generalized linear model plays an important role in statistical analysis and the related design issues are undoubtedly challenging. The state-of-the-art works mostly apply to design criteria on the estimates of regression coefficients. It is of importance to study optimal designs for generalized linear models, especially on the prediction aspects. In this work, we propose a prediction-oriented design criterion, I-optimality, and develop an efficient sequential algorithm of constructing I-optimal designs for generalized linear models. Through establishing the General Equivalence Theorem of the I-optimality for generalized linear models, we obtain an insightful understanding for the proposed algorithm on how to sequentially choose the support points and update the weights of support points of the design. The proposed algorithm is computationally efficient with guaranteed convergence property. Numerical examples are conducted to evaluate the feasibility and computational efficiency of the proposed algorithm. … **Regularized Determinantal Point Process (R-DPP)**

Given a fixed $n\times d$ matrix $\mathbf{X}$, where $n\gg d$, we study the complexity of sampling from a distribution over all subsets of rows where the probability of a subset is proportional to the squared volume of the parallelopiped spanned by the rows (a.k.a. a determinantal point process). In this task, it is important to minimize the preprocessing cost of the procedure (performed once) as well as the sampling cost (performed repeatedly). To that end, we propose a new determinantal point process algorithm which has the following two properties, both of which are novel: (1) a preprocessing step which runs in time $O(\text{number-of-non-zeros}(\mathbf{X})\cdot\log n)+\text{poly}(d)$, and (2) a sampling step which runs in $\text{poly}(d)$ time, independent of the number of rows $n$. We achieve this by introducing a new regularized determinantal point process (R-DPP), which serves as an intermediate distribution in the sampling procedure by reducing the number of rows from $n$ to $\text{poly}(d)$. Crucially, this intermediate distribution does not distort the probabilities of the target sample. Our key novelty in defining the R-DPP is the use of a Poisson random variable for controlling the probabilities of different subset sizes, leading to new determinantal formulas such as the normalization constant for this distribution. Our algorithm has applications in many diverse areas where determinantal point processes have been used, such as machine learning, stochastic optimization, data summarization and low-rank matrix reconstruction. … **Feature-Label Memory Network**

Deep learning typically requires training a very capable architecture using large datasets. However, many important learning problems demand an ability to draw valid inferences from small size datasets, and such problems pose a particular challenge for deep learning. In this regard, various researches on ‘meta-learning’ are being actively conducted. Recent work has suggested a Memory Augmented Neural Network (MANN) for meta-learning. MANN is an implementation of a Neural Turing Machine (NTM) with the ability to rapidly assimilate new data in its memory, and use this data to make accurate predictions. In models such as MANN, the input data samples and their appropriate labels from previous step are bound together in the same memory locations. This often leads to memory interference when performing a task as these models have to retrieve a feature of an input from a certain memory location and read only the label information bound to that location. In this paper, we tried to address this issue by presenting a more robust MANN. We revisited the idea of meta-learning and proposed a new memory augmented neural network by explicitly splitting the external memory into feature and label memories. The feature memory is used to store the features of input data samples and the label memory stores their labels. Hence, when predicting the label of a given input, our model uses its feature memory unit as a reference to extract the stored feature of the input, and based on that feature, it retrieves the label information of the input from the label memory unit. In order for the network to function in this framework, a new memory-writingmodule to encode label information into the label memory in accordance with the meta-learning task structure is designed. Here, we demonstrate that our model outperforms MANN by a large margin in supervised one-shot classification tasks using Omniglot and MNIST datasets. … **Decision Tree Based Missing Value Imputation Technique (DMI)**

Decision tree based Missing value Imputation technique’ (DMI) makes use of an EM algorithm and a decision tree (DT) algorithm. …

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Sep 2019

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