In the field of machine learning, hyperparameter optimization refers to the search for optimal hyperparameters. A hyperparameter is a parameter that is used to control the training algorithm and whose value, unlike other parameters, must be set before the model is actually trained. You can boost your machine learning Models with hyperparameter tuning/optimization. Hyperparameters contain the data that govern the training process itself. Your model parameters are optimized (you could say "tuned") by the training process: you run data through the operations of the model, compare the resulting prediction with the actual value for each data instance, evaluate the accuracy, and adjust until you find the best values.

Change detection in heterogeneous multitemporal satellite images is an emerging and challenging topic in remote sensing. In particular, one of the main challenges is to tackle the problem in an unsupervised manner. In this paper we propose an unsupervised framework for bitemporal heterogeneous change detection based on the comparison of affinity matrices and image regression. First, our method quantifies the similarity of affinity matrices computed from co-located image patches in the two images. This is done to automatically identify pixels that are likely to be unchanged. With the identified pixels as pseudo-training data, we learn a transformation to map the first image to the domain of the other image, and vice versa. Four regression methods are selected to carry out the transformation: Gaussian process regression, support vector regression, random forest regression, and a recently proposed kernel regression method called homogeneous pixel transformation. To evaluate the potentials and limitations of our framework, and also the benefits and disadvantages of each regression method, we perform experiments on two real data sets. The results indicate that the comparison of the affinity matrices can already be considered a change detection method by itself. However, image regression is shown to improve the results obtained by the previous step alone and produces accurate change detection maps despite of the heterogeneity of the multitemporal input data. Notably, the random forest regression approach excels by achieving similar accuracy as the other methods, but with a significantly lower computational cost and with fast and robust tuning of hyperparameters.

It was written as an advanced text to serve as a basis for a graduate course, and/or as a reference to the researcher diving into this fascinating world at the intersection of optimization and machine learning. Such a course was given at the Technion in the years 2010-2014 with slight variations from year to year, and later at Princeton University in the years 2015-2016. The core material in these courses is fully covered in this book, along with exercises that allow the students to complete parts of proofs, or that were found illuminating and thought-provoking. Most of the material is given with examples of applications, which are interlaced throughout different topics. These include prediction from expert advice, portfolio selection, matrix completion and recommendation systems, SVM training and more.

However, penalization approach requires one to solve the problem (2) for a sequence of the tuning parameter λ to obtain an entire solution path, thus yielding a considerable computational burden. Efron et al. [2004] showed that the optimal solution path of Lasso is piecewise linear and proposed LARS algorithm to compute the full solution path of Lasso efficiently. This result w as extended to more generic cases by Rosset and Zhu [2007] who derived a general c haracterization of the properties of (loss f, penalty ψ) pairs giving piecewise linear coefficient paths that allow for efficient generation of the full regulari zed coefficient paths.

Word embeddings capture semantic and syntactic similarities of words, represented as vectors. Word2Vec is a popular implementation of word embeddings; it takes as input a large corpus of text and learns a model that maps unique words in that corpus to other contextually relevant words. After training, Word2Vec's internal vector representation of words in the corpus map unique words to a vector space, which are then used in many downstream tasks. Training these models requires significant computational resources (training time often measured in days) and is difficult to parallelize. Most word embedding training uses stochastic gradient descent (SGD), an "inherently" sequential algorithm where at each step, the processing of the current example depends on the parameters learned from the previous examples. Prior approaches to parallelizing SGD do not honor these dependencies and thus potentially suffer poor convergence. This paper introduces GraphWord2Vec, a distributedWord2Vec algorithm which formulates the Word2Vec training process as a distributed graph problem and thus leverage state-of-the-art distributed graph analytics frameworks such as D-Galois and Gemini that scale to large distributed clusters. GraphWord2Vec also demonstrates how to use model combiners to honor data dependencies in SGD and thus scale without giving up convergence. We will show that GraphWord2Vec has linear scalability up to 32 machines converging as fast as a sequential run in terms of epochs, thus reducing training time by 14x.

We study the concentration of random kernel matrices around their mean. We derive nonasymptotic exponential concentration inequalities for Lipschitz kernels assuming that the data points are independent draws from a class of multivariate distributions on $\mathbb{R}^d$, including the strongly log-concave distributions under affine transformations. A feature of our result is that the data points need not have identical distributions or have zero mean, which is key in certain applications such as clustering. For comparison, we also derive the companion result for the Euclidean (inner product) kernel under a slightly modified set of distributional assumptions, more precisely, a class of sub-Gaussian vectors. A notable difference between the two cases is that, in contrast to the Euclidean kernel, in the Lipschitz case, the concentration inequality does not depend on the mean of the underlying vectors. As an application of these inequalities, we derive a bound on the misclassification rate of a kernel spectral clustering (KSC) algorithm, under a perturbed nonparametric mixture model. We show an example where this bound establishes the high-dimensional consistency (as $d \to \infty$) of the KSC, when applied with a Gaussian kernel, to a signal consisting of nested nonlinear manifolds (e.g., spheres) plus noise.

In this work, the possibility of clustering correlated random variables was examined, both because of their mutual similarity and because of their similarity to the principal components. The k-means algorithm and spectral algorithms were used for clustering. For spectral methods, the similarity matrix was both the matrix of relation established on the level of correlation and the matrix of coefficients of determination. For four different sets of data, different ways of measuring the disimilarity of variables were analyzed, and the impact of the diversity of initial points on the efficiency of the k-means algorithm was analyzed.

In remote sensing, it is often difficult to acquire or collect a large dataset that is accurately labeled. This difficulty is often due to several issues including but not limited to the study site's spatial area and accessibility, errors in global positioning system (GPS), and mixed pixels caused by an image's spatial resolution. An approach, with two variations, is proposed that estimates multiple target signatures from mixed training samples with imprecise labels: Multi-Target Multiple Instance Adaptive Cosine Estimator (Multi-Target MI-ACE) and Multi-Target Multiple Instance Spectral Match Filter (Multi-Target MI-SMF). The proposed methods address the problems above by directly considering the multiple-instance, imprecisely labeled dataset and learns a dictionary of target signatures that optimizes detection using the Adaptive Cosine Estimator (ACE) and Spectral Match Filter (SMF) against a background. The algorithms have two primary steps, initialization and optimization. The initialization process determines diverse target representatives, while the optimization process simultaneously updates the target representatives to maximize detection while learning the number of optimal signatures to describe the target class. Three designed experiments were done to test the proposed algorithms: a simulated hyperspectral dataset, the MUUFL Gulfport hyperspectral dataset collected over the University of Southern Mississippi-Gulfpark Campus, and the AVIRIS hyperspectral dataset collected over Santa Barbara County, California. Both simulated and real hyperspectral target detection experiments show the proposed algorithms are effective at learning target signatures and performing target detection.

In this work we propose a new method to optimize the architecture of an artificial neural network. The algorithm proposed, called Greedy Search for Neural Network Architecture, aims to minimize the complexity of the architecture search and the complexity of the final model selected without compromising the predictive performance. The reduction of the computational cost makes this approach appealing for two reasons. Firstly, there is a need from domain scientists to easily interpret predictions returned by a deep learning model and this tends to be cumbersome when neural networks have complex structures. Secondly, the use of neural networks is challenging in situations with compute/memory limitations. Promising numerical results show that our method is competitive against other hyperparameter optimization algorithms for attainable performance and computational cost. We also generalize the definition of adjusted score from linear regression models to neural networks. Numerical experiments are presented to show that the adjusted score can boost the greedy search to favor smaller architectures over larger ones without compromising the predictive performance.

We propose a new outline for dictionary learning methods based on a hierarchical clustering of the training data. Through recursive application of a clustering method the data is organized into a binary partition tree representing a multiscale structure. The dictionary atoms are defined adaptively based on the data clusters in the partition tree. This approach can be interpreted as a generalization of the wavelet transform. The computational bottleneck of the procedure is then the chosen clustering method: when using K-means the method runs much faster than K-SVD. Thanks to the multiscale properties of the partition tree, our dictionary is structured: when using Orthogonal Matching Pursuit to reconstruct patches from a natural image, dictionary atoms corresponding to nodes being closer to the root node in the tree have a tendency to be used with greater coefficients.