Regression is a statistical method for calculating relationships among variables. It is one of the most popular and simplest regression techniques and is a very good way to understand your data. Note that regression techniques are not 100% accurate even if you use higher-order (nonlinear) polynomials. The key with regression, as with most machine learning techniques, is to find a good-enough technique and not the perfect technique and model.

There are a lot of machine learning algorithm available and among them there are some which are used mostly among the use in daily cases. Some of the Machine Learning algorithm are mentioned.

This is a small tutorial on how to estimate prices of houses in Pharo using linear regression model from PolyMath. We will then visualize the data points together with the regression line using the new charting capabilities of Roassal3. The main purpose of this blog post is to demonstrate the new charting functionality of Roassal3 that were introduced yesterday. The visualization that we will build is not very pretty, but it will give you a taste of the amazing things that we will be able to do in the near future. Pharo is a pure object-oriented programming language and a powerful environment, focused on simplicity and immediate feedback (think IDE and OS rolled into one).

--Ensuring secure and reliable operations of the power grid is a primary concern of system operators. Phasor measurement units (PMUs) are rapidly being deployed in the grid to provide fast-sampled operational data that should enable quicker decision-making. This work presents a general interpretable framework for analyzing real-time PMU data, and thus enabling grid operators to understand the current state and to identify anomalies on the fly. Applying statistical learning tools on the streaming data, we first learn an effective dynamical model to describe the current behavior of the system. Next, we use the probabilistic predictions of our learned model to define in a principled way an efficient anomaly detection tool. Finally, the last module of our framework produces on-the-fly classification of the detected anomalies into common occurrence classes using features that grid operators are familiar with. We demonstrate the efficacy of our interpretable approach through extensive numerical experiments on real PMU data collected from a transmission operator in the USA. Traditional supervisory control and data acquisition (SCADA) systems provide information regarding the system state at the order of seconds to the operator. However, such fidelity, considered appropriate in prior decades, is not sufficient to observe or predict disturbances at faster timescales that are increasingly being observed in today's stochastic grid [1]. To provide more rapid measurement data, phasor measurement units (PMUs) have gained widespread deployment. PMUs [2] are time-synchronized by GPS timestamps and collect measurements of system states (Eg.

To address potential gaps noted in patient monitoring in the hospital, a novel patient behavior detection system using mmWave radar and deep convolution neural network (CNN), which supports the simultaneous recognition of multiple patients' behaviors in real-time, is proposed. In this study, we use an mmWave radar to track multiple patients and detect the scattering point cloud of each one. For each patient, the Doppler pattern of the point cloud over a time period is collected as the behavior signature. A three-layer CNN model is created to classify the behavior for each patient. The tracking and point clouds detection algorithm was also implemented on an mmWave radar hardware platform with an embedded graphics processing unit (GPU) board to collect Doppler pattern and run the CNN model. A training dataset of six types of behavior were collected, over a long duration, to train the model using Adam optimizer with an objective to minimize cross-entropy loss function. Lastly, the system was tested for real-time operation and obtained a very good inference accuracy when predicting each patient's behavior in a two-patient scenario.

In this paper, we present experimental results obtained from retraining the last layer of the Inception v3 model in classifying images of human faces into one of five basic face shapes. The accuracy of the retrained Inception v3 model was compared with that of the following classification methods that uses facial landmark distance ratios and angles as features: linear discriminant analysis (LDA), support vector machines with linear kernel (SVM-LIN), support vector machines with radial basis function kernel (SVM-RBF), artificial neural networks or multilayer perceptron (MLP), and k-nearest neighbors (KNN). All classifiers were trained and tested using a total of 500 images of female celebrities with known face shapes collected from the Internet. Results show that training accuracy and overall accuracy ranges from 98.0% to 100% and from 84.4% to 84.8% for Inception v3 and from 50.6% to 73.0% and from 36.4% to 64.6% for the other classifiers depending on the training set size used. This result shows that the retrained Inception v3 model was able to fit the training data well and outperform the other classifiers without the need to handpick specific features to include in model training. Future work should consider expanding the labeled dataset, preferably one that can also be freely distributed to the research community, so that proper model cross-validation can be performed. As far as we know, this is the first in the literature to use convolutional neural networks in face-shape classification. The scripts are available at https://github.com/adonistio/inception-face-shape-classifier.

During the last decades, learning a low-dimensional space with discriminative information for dimension reduction (DR) has gained a surge of interest. However, it's not accessible for these DR methods to achieve satisfactory performance when facing the features from multiple views. In multi-view learning problems, one instance can be represented by multiple heterogeneous features, which are highly related but sometimes look different from each other. In addition, correlations between features from multiple views always vary greatly, which challenges the capability of multi-view learning methods. Consequently, constructing a multi-view learning framework with generalization and scalability, which could take advantage of multi-view information as much as possible, is extremely necessary but challenging. To implement the above target, this paper proposes a novel multi-view learning framework based on similarity consensus, which makes full use of correlations among multi-view features while considering the scalability and robustness of the framework. It aims to straightforwardly extend those existing DR methods into multi-view learning domain by preserving the similarity between different views to capture the low-dimensional embedding. Two schemes based on pairwise-consensus and centroid-consensus are separately proposed to force multiple views to learn from each other and then an iterative alternating strategy is developed to obtain the optimal solution. The proposed method is evaluated on 5 benchmark datasets and comprehensive experiments show that our proposed multi-view framework can yield comparable and promising performance with previous approaches proposed in recent literatures.

Jerry Quinn IBM T.J. Watson Research Center Y orktown Heights, NY 10598 V alentina Salapura IBM T.J. Watson Research Center Y orktown Heights, NY 10598 Abstract This paper presents a methodology for selecting the mini-batch size that minimizes Stochastic Gradient Descent (SGD) learning time for single and multiple learner problems. By de-coupling algorithmic analysis issues from hardware and software implementation details, we reveal a robust empirical inverse law between mini-batch size and the average number of SGD updates required to converge to a specified error threshold. Combining this empirical inverse law with measured system performance, we create an accurate, closed-form model of average training time and show how this model can be used to identify quantifiable implications for both algorithmic and hardware aspects of machine learning. We demonstrate the inverse law empirically, on both image recognition (MNIST, CIFAR10 and CIFAR100) and machine translation (Europarl) tasks, and provide a theoretic justification via proving a novel bound on mini-batch SGD training. Introduction In this paper, we present an empirical law, with theoretical justification, linking the number of learning iterations to the mini-batch size. From this result, we derive a principled methodology for selecting mini-batch size w.r.t. This methodology saves training time and provides both intuition and a principled approach for optimizing machine learning algorithms and machine learning hardware system design. Further, we use our methodology to show that focusing on weak scaling can lead to suboptimal training times because, by neglecting the dependence of convergence time on the size of the mini-batch used, weak scaling does not always minimize the training time.

Multi-output Gaussian processes (MOGPs) leverage the flexibility and interpretability of GPs while capturing structure across outputs, which is desirable, for example, in spatio-temporal modelling. The key problem with MOGPs is the cubic computational scaling in the number of both inputs (e.g., time points or locations), n, and outputs, p. Current methods reduce this to O(n^3 m^3), where m < p is the desired degrees of freedom. This computational cost, however, is still prohibitive in many applications. To address this limitation, we present the Orthogonal Linear Mixing Model (OLMM), an MOGP in which exact inference scales linearly in m: O(n^3 m). This advance opens up a wide range of real-world tasks and can be combined with existing GP approximations in a plug-and-play way as demonstrated in the paper. Additionally, the paper organises the existing disparate literature on MOGP models into a simple taxonomy called the Mixing Model Hierarchy (MMH).

We propose a regression algorithm that utilizes a learned dictionary optimized for sparse inference on D-Wave quantum annealer. In this regression algorithm, we concatenate the independent and dependent variables as an combined vector, and encode the high-order correlations between them into a dictionary optimized for sparse reconstruction. On a test dataset, the dependent variable is initialized to its average value and then a sparse reconstruction of the combined vector is obtained in which the dependent variable is typically shifted closer to its true value, as in a standard inpainting or denoising task. Here, a quantum annealer, which can presumably exploit a fully entangled initial state to better explore the complex energy landscape, is used to solve the highly non-convex sparse coding optimization problem. The regression algorithm is demonstrated for a lattice quantum chromodynamics simulation data using a D-Wave 2000Q quantum annealer and good prediction performance is achieved. The regression test is performed using six different values for the number of fully connected logical qubits, between 20 and 64, the latter being the maximum that can be embedded on the D-Wave 2000Q. The scaling results indicate that a larger number of qubits gives better prediction accuracy, the best performance being comparable to the best classical regression algorithms reported so far.