Research by Hubel and Wiesel [2,3] analyzed the striate cortex of cats and monkeys, revealing two key findings that would come to heavily influence Fukushima's work [1]. The next significant implementation of a convolution neural network was LeNet-5 proposed in 1999 by Le Cun et al. in their work "Object Recognition with Gradient Based Learning'' [4]. Their proposed network, LeNet-5 performed well on the MNIST data set and was shown to do better than state of the art (at the time) SVMs and K-nearest neighbor based approaches. Their final implementation outperformed other state of the art image classification algorithms with error rates which were 10% lower than its competitors on the ImageNet dataset. This application of a discrete convolution precisely represents local receptive fields observed by Hubel and Wiesel [2,3] and implemented in early CNNs by Fukushima and Le Cun [1,4]. Research by Hubel and Wiesel [2,3] analyzed the striate cortex of cats and monkeys, revealing two key findings that would come to heavily influence Fukushima's work [1]. The next significant implementation of a convolution neural network was LeNet-5 proposed in 1999 by Le Cun et al. in their work "Object Recognition with Gradient Based Learning'' [4].

To make it more clear why collinearity is such a problem, let's take a look at a use case. For the use case, I am going to use the car dataset that you can download easily on Kaggle. Let's imagine we want to predict the price of a car, or price variable in the dataset. To predict it, we will use certain independent variables such as the car's city MPG, highway MPG, horsepower, engine size, stroke, width, peak RPM, and compression ratio. Next, we build a regression model based on these independent variables.

Machine Learning is the path to a better and advanced future. A Machine Learning Developer is the most demanding job in 2021, and it is going to increase by 20–30% in the upcoming 3–5 years. Machine Learning by the core is all statistics and programming concepts. The language that is mostly used by Machine learning developers for coding is python because of its simplicity. In this blog, you will find some of the most asked machine learning questions that every machine learning enthusiast has to answer one day. Ans: Machine learning is the science of getting computers to act in a real-time situation without being explicitly programmed.

Sketches are a medium to convey a visual scene from an individual's creative perspective. The addition of color substantially enhances the overall expressivity of a sketch. This paper proposes two methods to mimic human-drawn colored sketches by utilizing the Contour Drawing Dataset. Our first approach renders colored outline sketches by applying image processing techniques aided by k-means color clustering. The second method uses a generative adversarial network to develop a model that can generate colored sketches from previously unobserved images. We assess the results obtained through quantitative and qualitative evaluations.

Starting from finding approximate value of a function, introduces the measure of approximation-degree between two numerical values, proposes the concepts of "strict approximation" and "strict approximation region", then, derives the corresponding one-dimensional interpolation methods and formulas, and then presents a calculation model called "sum-times-difference formula" for high-dimensional interpolation, thus develops a new interpolation approach, that is, ADB interpolation. ADB interpolation is applied to the interpolation of actual functions with satisfactory results. Viewed from principle and effect, the interpolation approach is of novel idea, and has the advantages of simple calculation, stable accuracy, facilitating parallel processing, very suiting for high-dimensional interpolation, and easy to be extended to the interpolation of vector valued functions. Applying the approach to instance-based learning, a new instance-based learning method, learning using ADB interpolation, is obtained. The learning method is of unique technique, which has also the advantages of definite mathematical basis, implicit distance weights, avoiding misclassification, high efficiency, and wide range of applications, as well as being interpretable, etc. In principle, this method is a kind of learning by analogy, which and the deep learning that belongs to inductive learning can complement each other, and for some problems, the two can even have an effect of "different approaches but equal results" in big data and cloud computing environment. Thus, the learning using ADB interpolation can also be regarded as a kind of "wide learning" that is dual to deep learning.

The integration of learning and reasoning is one of the key challenges in artificial intelligence and machine learning today, and various communities have been addressing it. That is especially true for the field of neural-symbolic computation (NeSy) [10, 21], where the goal is to integrate symbolic reasoning and neural networks. NeSy already has a long tradition, and it has recently attracted a lot of attention from various communities (cf. the keynotes of Y. Bengio and H. Kautz on this topic at AAAI 2020, the AI Debate [9] between Y. Bengio and G. Marcus). Another domain that has a rich tradition in integrating learning and reasoning is that of statistical relational learning and artificial intelligence (StarAI) [39, 85]. But rather than focusing on integrating logic and neural networks, it is centred around the question of integrating logic with probabilistic reasoning, more specifically probabilistic graphical models. Despite the common interest in combining symbolic reasoning with a basic paradigm for learning, i.e., probabilistic graphical models or neural networks, it is surprising that there are not more interactions between these two fields.

Federated learning (FL) is an emerging privacy preserving machine learning protocol that allows multiple devices to collaboratively train a shared global model without revealing their private local data. Non-parametric models like gradient boosting decision trees (GBDT) have been commonly used in FL for vertically partitioned data. However, all these studies assume that all the data labels are stored on only one client, which may be unrealistic for real-world applications. Therefore, in this work, we propose a secure vertical FL framework, named PIVODL, to train GBDT with data labels distributed on multiple devices. Both homomorphic encryption and differential privacy are adopted to prevent label information from being leaked through transmitted gradients and leaf values. Our experimental results show that both information leakage and model performance degradation of the proposed PIVODL are negligible.

The recent success of neural network models has shone light on a rather surprising statistical phenomenon: statistical models that perfectly fit noisy data can generalize well to unseen test data. Understanding this phenomenon of $\textit{benign overfitting}$ has attracted intense theoretical and empirical study. In this paper, we consider interpolating two-layer linear neural networks trained with gradient flow on the squared loss and derive bounds on the excess risk when the covariates satisfy sub-Gaussianity and anti-concentration properties, and the noise is independent and sub-Gaussian. By leveraging recent results that characterize the implicit bias of this estimator, our bounds emphasize the role of both the quality of the initialization as well as the properties of the data covariance matrix in achieving low excess risk.

We consider the task of heavy-tailed statistical estimation given streaming $p$-dimensional samples. This could also be viewed as stochastic optimization under heavy-tailed distributions, with an additional $O(p)$ space complexity constraint. We design a clipped stochastic gradient descent algorithm and provide an improved analysis, under a more nuanced condition on the noise of the stochastic gradients, which we show is critical when analyzing stochastic optimization problems arising from general statistical estimation problems. Our results guarantee convergence not just in expectation but with exponential concentration, and moreover does so using $O(1)$ batch size. We provide consequences of our results for mean estimation and linear regression. Finally, we provide empirical corroboration of our results and algorithms via synthetic experiments for mean estimation and linear regression.

I recently fell in love with Explainable AI (XAI). XAI is a set of methods aimed at making increasingly complex machine learning (ML) models understandable by humans. XAI could help bridge the gap between AI and humans. That is very much needed as the gap is widening. Machine learning is proving incredibly successful in tackling problems from cancer diagnostics to fraud detection.