Linear Regression is a statistical method used for modelling the dependence or relationship between two or more quantities. The aim of this is to be able to either better understand the existing relationships or to be able to predict the behaviour at points for which we currently don't have data. By using the method of linear regression (also called least squares fitting), we can calculate the values for the two parameters and plot the line of best fit to achieve our aims of better understanding the relationship or finding the estimated values of unknown points. For this, we have to be able to calculate the slope (m) and intercept (c) to give us the line of best fit for the data. This is made simple however by libraries that have already been implemented such as Scikit-Learn and Statsmodels Api that have linear regression functionality built in.

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Human beings so easily perceive the visual surroundings, it doesn't require any effort. It is like instantly interpreting the visual information we see without even being bothered as to how we understand? But making machines see is not easy and requires a lot of work. Lots of research and efforts have been undertaken and are ongoing to make the systems understand the visual inputs just like human beings. Computer vision (CV) is a field of AI that provides the capability to the devices to interpret visual inputs like images and videos.

We'll be comparing the results of all the algorithms and making a good analytical approach. What are you waiting for?

The increasing automation in many areas of the Industry expressly demands to design efficient machine-learning solutions for the detection of abnormal events. With the ubiquitous deployment of sensors monitoring nearly continuously the health of complex infrastructures, anomaly detection can now rely on measurements sampled at a very high frequency, providing a very rich representation of the phenomenon under surveillance. In order to exploit fully the information thus collected, the observations cannot be treated as multivariate data anymore and a functional analysis approach is required. It is the purpose of this paper to investigate the performance of recent techniques for anomaly detection in the functional setup on real datasets. After an overview of the state-of-the-art and a visual-descriptive study, a variety of anomaly detection methods are compared. While taxonomies of abnormalities (e.g. shape, location) in the functional setup are documented in the literature, assigning a specific type to the identified anomalies appears to be a challenging task. Thus, strengths and weaknesses of the existing approaches are benchmarked in view of these highlighted types in a simulation study. Anomaly detection methods are next evaluated on two datasets, related to the monitoring of helicopters in flight and to the spectrometry of construction materials namely. The benchmark analysis is concluded by recommendation guidance for practitioners.

The detection and estimation of sinusoids is a fundamental signal processing task for many applications related to sensing and communications. While algorithms have been proposed for this setting, quantization is a critical, but often ignored modeling effect. In wireless communications, estimation with low resolution data converters is relevant for reduced power consumption in wideband receivers. Similarly, low resolution sampling in imaging and spectrum sensing allows for efficient data collection. In this work, we propose SignalNet, a neural network architecture that detects the number of sinusoids and estimates their parameters from quantized in-phase and quadrature samples. We incorporate signal reconstruction internally as domain knowledge within the network to enhance learning and surpass traditional algorithms in mean squared error and Chamfer error. We introduce a worst-case learning threshold for comparing the results of our network relative to the underlying data distributions. This threshold provides insight into why neural networks tend to outperform traditional methods and into the learned relationships between the input and output distributions. In simulation, we find that our algorithm is always able to surpass the threshold for three-bit data but often cannot exceed the threshold for one-bit data. We use the learning threshold to explain, in the one-bit case, how our estimators learn to minimize the distributional loss, rather than learn features from the data.

Multi-block CCA constructs linear relationships explaining coherent variations across multiple blocks of data. We view the multi-block CCA problem as finding leading generalized eigenvectors and propose to solve it via a proximal gradient descent algorithm with $\ell_1$ constraint for high dimensional data. In particular, we use a decaying sequence of constraints over proximal iterations, and show that the resulting estimate is rate-optimal under suitable assumptions. Although several previous works have demonstrated such optimality for the $\ell_0$ constrained problem using iterative approaches, the same level of theoretical understanding for the $\ell_1$ constrained formulation is still lacking. We also describe an easy-to-implement deflation procedure to estimate multiple eigenvectors sequentially. We compare our proposals to several existing methods whose implementations are available on R CRAN, and the proposed methods show competitive performances in both simulations and a real data example.

Statistical depths provide a fundamental generalization of quantiles and medians to data in higher dimensions. This paper proposes a new type of globally defined statistical depth, based upon control theory and eikonal equations, which measures the smallest amount of probability density that has to be passed through in a path to points outside the support of the distribution: for example spatial infinity. This depth is easy to interpret and compute, expressively captures multi-modal behavior, and extends naturally to data that is non-Euclidean. We prove various properties of this depth, and provide discussion of computational considerations. In particular, we demonstrate that this notion of depth is robust under an aproximate isometrically constrained adversarial model, a property which is not enjoyed by the Tukey depth. Finally we give some illustrative examples in the context of two-dimensional mixture models and MNIST.

Hyperparameter plays an essential role in the fitting of supervised machine learning algorithms. However, it is computationally expensive to tune all the tunable hyperparameters simultaneously especially for large data sets. In this paper, we give a definition of hyperparameter importance that can be estimated by subsampling procedures. According to the importance, hyperparameters can then be tuned on the entire data set more efficiently. We show theoretically that the proposed importance on subsets of data is consistent with the one on the population data under weak conditions. Numerical experiments show that the proposed importance is consistent and can save a lot of computational resources.

Despite recent progress made by self-supervised methods in representation learning with residual networks, they still underperform supervised learning on the ImageNet classification benchmark, limiting their applicability in performance-critical settings. Building on prior theoretical insights from Mitrovic et al., 2021, we propose ReLICv2 which combines an explicit invariance loss with a contrastive objective over a varied set of appropriately constructed data views. ReLICv2 achieves 77.1% top-1 classification accuracy on ImageNet using linear evaluation with a ResNet50 architecture and 80.6% with larger ResNet models, outperforming previous state-of-the-art self-supervised approaches by a wide margin. Most notably, ReLICv2 is the first representation learning method to consistently outperform the supervised baseline in a like-for-like comparison using a range of standard ResNet architectures. Finally we show that despite using ResNet encoders, ReLICv2 is comparable to state-of-the-art self-supervised vision transformers.