The objective of this work is to study the applicability of various Machine Learning algorithms for prediction of some rock properties which geoscientists usually define due to special lab analysis. We demonstrate that these special properties can be predicted only basing on routine core analysis (RCA) data. To validate the approach core samples from the reservoir with soluble rock matrix components (salts) were tested within 100+ laboratory experiments. The challenge of the experiments was to characterize the rate of salts in cores and alteration of porosity and permeability after reservoir desalination due to drilling mud or water injection. For these three measured characteristics, we developed the relevant predictive models, which were based on the results of RCA and data on coring depth and top and bottom depths of productive horizons. To select the most accurate Machine Learning algorithm a comparative analysis has been performed. It was shown that different algorithms work better in different models. However, two hidden layers Neural network has demonstrated the best predictive ability and generalizability for all three rock characteristics jointly. The other algorithms, such as Support Vector Machine and Linear Regression, also worked well on the dataset, but in particular cases. Overall, the applied approach allows predicting the alteration of porosity and permeability during desalination in porous rocks and also evaluating salt concentration without direct measurements in a laboratory. This work also shows that developed approaches could be applied for prediction of other rock properties (residual brine and oil saturations, relative permeability, capillary pressure, and others), which laboratory measurements are time-consuming and expensive.

Other than the various cross-validation functions, the main functions are polyfit() and predict.polyFit(). One can fit either regression or classification models, with an option to perform PCA for dimension reduction on the predictors/features. Built in to the latest version of the regtools package. In the former case, getPE() reads in the dataset and does some preprocessing, producing a data frame pe. Forward stepwise regression is also available with FSR which also accepts polynomial degree and interaction as inputs.

I recently took Andrew Ng's Machine Learning course on Coursera, and I'm hoping to write a series of blog posts on what I learnt. In these we will look at a variety of machine learning techniques and categories, starting with linear and logistic regression. Machine learning is something of a buzzword at the moment, but underneath all the hype it's a technology that's expected to revolutionise virtually all industries, and have a huge impact on people's lives in the coming decades. Machine learning problems can be split into supervised learning and unsupervised learning. Supervised learning works by giving the algorithm the "right answers", which are used to train the algorithm so that it can fit and predict when given new examples.

We propose a novel exponentially-modified Gaussian (EMG) mixture residual model. The EMG mixture is well suited to model residuals that are contaminated by a distribution with positive support. This is in contrast to commonly used robust residual models, like the Huber loss or $\ell_1$, which assume a symmetric contaminating distribution and are otherwise asymptotically biased. We propose an expectation-maximization algorithm to optimize an arbitrary model with respect to the EMG mixture. We apply the approach to linear regression and probabilistic matrix factorization (PMF). We compare against other residual models, including quantile regression. Our numerical experiments demonstrate the strengths of the EMG mixture on both tasks. The PMF model arises from considering spectroscopic data. In particular, we demonstrate the effectiveness of PMF in conjunction with the EMG mixture model on synthetic data and two real-world applications: X-ray diffraction and Raman spectroscopy. We show how our approach is effective in inferring background signals and systematic errors in data arising from these experimental settings, dramatically outperforming existing approaches and revealing the data's physically meaningful components.

We study online linear regression problems in a distributed setting, where the data is spread over a network. In each round, each network node proposes a linear predictor, with the objective of fitting the \emph{network-wide} data. It then updates its predictor for the next round according to the received local feedback and information received from neighboring nodes. The predictions made at a given node are assessed through the notion of regret, defined as the difference between their cumulative network-wide square errors and those of the best off-line network-wide linear predictor. Various scenarios are investigated, depending on the nature of the local feedback (full information or bandit feedback), on the set of available predictors (the decision set), and the way data is generated (by an oblivious or adaptive adversary). We propose simple and natural distributed regression algorithms, involving, at each node and in each round, a local gradient descent step and a communication and averaging step where nodes aim at aligning their predictors to those of their neighbors. We establish regret upper bounds typically in ${\cal O}(T^{3/4})$ when the decision set is unbounded and in ${\cal O}(\sqrt{T})$ in case of bounded decision set.

In this work we provide a theoretical framework for structured prediction that generalizes the existing theory of surrogate methods for binary and multiclass classification based on estimating conditional probabilities with smooth convex surrogates (e.g. logistic regression). The theory relies on a natural characterization of structural properties of the task loss and allows to derive statistical guarantees for many widely used methods in the context of multilabeling, ranking, ordinal regression and graph matching. In particular, we characterize the smooth convex surrogates compatible with a given task loss in terms of a suitable Bregman divergence composed with a link function. This allows to derive tight bounds for the calibration function and to obtain novel results on existing surrogate frameworks for structured prediction such as conditional random fields and quadratic surrogates.

Today's AI still faces two major challenges. One is that in most industries, data exists in the form of isolated islands. The other is the strengthening of data privacy and security. We propose a possible solution to these challenges: secure federated learning. Beyond the federated learning framework first proposed by Google in 2016, we introduce a comprehensive secure federated learning framework, which includes horizontal federated learning, vertical federated learning and federated transfer learning. We provide definitions, architectures and applications for the federated learning framework, and provide a comprehensive survey of existing works on this subject. In addition, we propose building data networks among organizations based on federated mechanisms as an effective solution to allow knowledge to be shared without compromising user privacy.

Data privacy is an important concern in machine learning, and is fundamentally at odds with the task of training useful learning models, which typically require the acquisition of large amounts of private user data. One possible way of fulfilling the machine learning task while preserving user privacy is to train the model on a transformed, noisy version of the data, which does not reveal the data itself directly to the training procedure. In this work, we analyze the privacy-utility trade-off of two such schemes for the problem of linear regression: additive noise, and random projections. In contrast to previous work, we consider a recently proposed notion of differential privacy that is based on conditional mutual information (MI-DP), which is stronger than the conventional $(\epsilon, \delta)$-differential privacy, and use relative objective error as the utility metric. We find that projecting the data to a lower-dimensional subspace before adding noise attains a better trade-off in general. We also make a connection between privacy problem and (non-coherent) SIMO, which has been extensively studied in wireless communication, and use tools from there for the analysis. We present numerical results demonstrating the performance of the schemes.

We prove that α-loss has an equivalent margin-based form and is classification-calibrated, two desirable properties for a good surrogate loss function for the ideal yet intractable 0-1 loss. For logistic regression-based classification, we provide an upper bound on the difference between the empirical and expected risk for α-loss by exploiting its Lipschitzianity along with recent results on the landscape features of empirical risk functions. Finally, we show that α-loss with α 2 performs better than log-loss on MNIST for logistic regression. I. INTRODUCTION In learning theory, the performance of a classification algorithm interms of accuracy, tractability, and convergence guarantees is contingent on the choice of a loss function. Consider a feature vector X X, an unknown finite label Y Y, and a hypothesis test h: X Y. The canonical 0-1 loss, given by 1[h(X) Y ], is considered an ideal loss function that captures the probability of incorrectly guessing the true label Y using h(X).

Privacy-preserving data analysis is a rising challenge in contemporary statistics, as the privacy guarantees of statistical methods are often achieved at the expense of accuracy. In this paper, we investigate the tradeoff between statistical accuracy and privacy in mean estimation and linear regression, under both the classical low-dimensional and modern high-dimensional settings. A primary focus is to establish minimax optimality for statistical estimation with the $(\varepsilon,\delta)$-differential privacy constraint. To this end, we find that classical lower bound arguments fail to yield sharp results, and new technical tools are called for. We first develop a general lower bound argument for estimation problems with differential privacy constraints, and then apply the lower bound argument to mean estimation and linear regression. For these statistical problems, we also design computationally efficient algorithms that match the minimax lower bound up to a logarithmic factor. In particular, for the high-dimensional linear regression, a novel private iterative hard thresholding pursuit algorithm is proposed, based on a privately truncated version of stochastic gradient descent. The numerical performance of these algorithms is demonstrated by simulation studies and applications to real data containing sensitive information, for which privacy-preserving statistical methods are necessary.