The variable you want to predict is called the dependent variable. The variable you are using to predict the other variable's value is called the independent variable. K-NN is a non-parametric algorithm, which means it does not make any assumption on underlying data. It is also called a lazy learner algorithm because it does not learn from the training set immediately instead it stores the dataset and at the time of classification, it performs an action on the dataset. The Naive Bayes classification algorithm is a probabilistic classifier.

I will be using Keras and TensorFlow to train a deep neural network to predict the grade using 2 hidden layers, mean squared error loss, and an RMSprop optimizer. Let's graph the error and the loss during training and evaluate the model We are getting a 0.69 mean absolute error with this approach. We also need to save the model to deploy it in an API. Since I am using google Colab I can easily save it to google drive. Initialize a random forest with 100 decision trees and train it on the same data.

We consider the Bayesian calibration of models describing the phenomenon of block copolymer (BCP) self-assembly using image data produced by microscopy or X-ray scattering techniques. To account for the random long-range disorder in BCP equilibrium structures, we introduce auxiliary variables to represent this aleatory uncertainty. These variables, however, result in an integrated likelihood for high-dimensional image data that is generally intractable to evaluate. We tackle this challenging Bayesian inference problem using a likelihood-free approach based on measure transport together with the construction of summary statistics for the image data. We also show that expected information gains (EIGs) from the observed data about the model parameters can be computed with no significant additional cost. Lastly, we present a numerical case study based on the Ohta--Kawasaki model for diblock copolymer thin film self-assembly and top-down microscopy characterization. For calibration, we introduce several domain-specific energy- and Fourier-based summary statistics, and quantify their informativeness using EIG. We demonstrate the power of the proposed approach to study the effect of data corruptions and experimental designs on the calibration results.

One of the significant challenges that smart grid networks face is cyber-security. Several studies have been conducted to highlight those security challenges. However, the majority of these surveys classify attacks based on the security requirements, confidentiality, integrity, and availability, without taking into consideration the accountability requirement. In addition, some of these surveys focused on the Transmission Control Protocol/Internet Protocol (TCP/IP) model, which does not differentiate between the application, session, and presentation and the data link and physical layers of the Open System Interconnection (OSI) model. In this survey paper, we provide a classification of attacks based on the OSI model and discuss in more detail the cyber-attacks that can target the different layers of smart grid networks communication. We also propose new classifications for the detection and countermeasure techniques and describe existing techniques under each category. Finally, we discuss challenges and future research directions.

Unsupervised person re-identification is a challenging and promising task in computer vision. Nowadays unsupervised person re-identification methods have achieved great progress by training with pseudo labels. However, how to purify feature and label noise is less explicitly studied in the unsupervised manner. To purify the feature, we take into account two types of additional features from different local views to enrich the feature representation. The proposed multi-view features are carefully integrated into our cluster contrast learning to leverage more discriminative cues that the global feature easily ignored and biased. To purify the label noise, we propose to take advantage of the knowledge of teacher model in an offline scheme. Specifically, we first train a teacher model from noisy pseudo labels, and then use the teacher model to guide the learning of our student model. In our setting, the student model could converge fast with the supervision of the teacher model thus reduce the interference of noisy labels as the teacher model greatly suffered. After carefully handling the noise and bias in the feature learning, our purification modules are proven to be very effective for unsupervised person re-identification. Extensive experiments on three popular person re-identification datasets demonstrate the superiority of our method. Especially, our approach achieves a state-of-the-art accuracy 85.8\% @mAP and 94.5\% @Rank-1 on the challenging Market-1501 benchmark with ResNet-50 under the fully unsupervised setting. The code will be released.

Low dimensional and computationally less expensive Reduced-Order Models (ROMs) have been widely used to capture the dominant behaviors of high-dimensional systems. A ROM can be obtained, using the well-known Proper Orthogonal Decomposition (POD), by projecting the full-order model to a subspace spanned by modal basis modes which are learned from experimental, simulated or observational data, i.e., training data. However, the optimal basis can change with the parameter settings. When a ROM, constructed using the POD basis obtained from training data, is applied to new parameter settings, the model often lacks robustness against the change of parameters in design, control, and other real-time operation problems. This paper proposes to use regression trees on Grassmann Manifold to learn the mapping between parameters and POD bases that span the low-dimensional subspaces onto which full-order models are projected. Motivated by the fact that a subspace spanned by a POD basis can be viewed as a point in the Grassmann manifold, we propose to grow a tree by repeatedly splitting the tree node to maximize the Riemannian distance between the two subspaces spanned by the predicted POD bases on the left and right daughter nodes. Five numerical examples are presented to comprehensively demonstrate the performance of the proposed method, and compare the proposed tree-based method to the existing interpolation method for POD basis and the use of global POD basis. The results show that the proposed tree-based method is capable of establishing the mapping between parameters and POD bases, and thus adapt ROMs for new parameters.

Bilevel optimization have gained growing interests, with numerous applications found in meta learning, minimax games, reinforcement learning, and nested composition optimization. This paper studies the problem of distributed bilevel optimization over a network where agents can only communicate with neighbors, including examples from multi-task, multi-agent learning and federated learning. In this paper, we propose a gossip-based distributed bilevel learning algorithm that allows networked agents to solve both the inner and outer optimization problems in a single timescale and share information via network propagation. We show that our algorithm enjoys the $\mathcal{O}(\frac{1}{K \epsilon^2})$ per-agent sample complexity for general nonconvex bilevel optimization and $\mathcal{O}(\frac{1}{K \epsilon})$ for strongly convex objective, achieving a speedup that scales linearly with the network size. The sample complexities are optimal in both $\epsilon$ and $K$. We test our algorithm on the examples of hyperparameter tuning and decentralized reinforcement learning. Simulated experiments confirmed that our algorithm achieves the state-of-the-art training efficiency and test accuracy.

Using representations of functional data can be more convenient and beneficial in subsequent statistical models than direct observations. These representations, in a lower-dimensional space, extract and compress information from individual curves. The existing representation learning approaches in functional data analysis usually use linear mapping in parallel to those from multivariate analysis, e.g., functional principal component analysis (FPCA). However, functions, as infinite-dimensional objects, sometimes have nonlinear structures that cannot be uncovered by linear mapping. Linear methods will be more overwhelmed given multivariate functional data. For that matter, this paper proposes a functional nonlinear learning (FunNoL) method to sufficiently represent multivariate functional data in a lower-dimensional feature space. Furthermore, we merge a classification model for enriching the ability of representations in predicting curve labels. Hence, representations from FunNoL can be used for both curve reconstruction and classification. Additionally, we have endowed the proposed model with the ability to address the missing observation problem as well as to further denoise observations. The resulting representations are robust to observations that are locally disturbed by uncontrollable random noises. We apply the proposed FunNoL method to several real data sets and show that FunNoL can achieve better classifications than FPCA, especially in the multivariate functional data setting. Simulation studies have shown that FunNoL provides satisfactory curve classification and reconstruction regardless of data sparsity.

Recent progress in center-based clustering algorithms combats poor local minima by implicit annealing, using a family of generalized means. These methods are variations of Lloyd's celebrated $k$-means algorithm, and are most appropriate for spherical clusters such as those arising from Gaussian data. In this paper, we bridge these algorithmic advances to classical work on hard clustering under Bregman divergences, which enjoy a bijection to exponential family distributions and are thus well-suited for clustering objects arising from a breadth of data generating mechanisms. The elegant properties of Bregman divergences allow us to maintain closed form updates in a simple and transparent algorithm, and moreover lead to new theoretical arguments for establishing finite sample bounds that relax the bounded support assumption made in the existing state of the art. Additionally, we consider thorough empirical analyses on simulated experiments and a case study on rainfall data, finding that the proposed method outperforms existing peer methods in a variety of non-Gaussian data settings.

We study the efficiency of Thompson sampling for contextual bandits. Existing Thompson sampling-based algorithms need to construct a Laplace approximation (i.e., a Gaussian distribution) of the posterior distribution, which is inefficient to sample in high dimensional applications for general covariance matrices. Moreover, the Gaussian approximation may not be a good surrogate for the posterior distribution for general reward generating functions. We propose an efficient posterior sampling algorithm, viz., Langevin Monte Carlo Thompson Sampling (LMC-TS), that uses Markov Chain Monte Carlo (MCMC) methods to directly sample from the posterior distribution in contextual bandits. Our method is computationally efficient since it only needs to perform noisy gradient descent updates without constructing the Laplace approximation of the posterior distribution. We prove that the proposed algorithm achieves the same sublinear regret bound as the best Thompson sampling algorithms for a special case of contextual bandits, viz., linear contextual bandits. We conduct experiments on both synthetic data and real-world datasets on different contextual bandit models, which demonstrates that directly sampling from the posterior is both computationally efficient and competitive in performance.