Neural networks achieve outstanding accuracy in classification and regression tasks. However, understanding their behavior still remains an open challenge that requires questions to be addressed on the robustness, explainability and reliability of predictions. We answer these questions by computing reachable sets of neural networks, i.e. sets of outputs resulting from continuous sets of inputs. We provide two efficient approaches that lead to over- and under-approximations of the reachable set. This principle is highly versatile, as we show. First, we analyze and enhance the robustness properties of both classifiers and regression models. This is in contrast to existing works, which only handle classification. Specifically, we verify (non-)robustness, propose a robust training procedure, and show that our approach outperforms adversarial attacks as well as state-of-the-art methods of verifying classifiers for non-norm bound perturbations. We also provide a technique of distinguishing between reliable and non-reliable predictions for unlabeled inputs, quantify the influence of each feature on a prediction, and compute a feature ranking.

Human behavior has exceptionally great reserves of knowledge and technology. We are trying to understand and generate as much as we can from human brains. I feel one of the breakthroughs in maneuvering the human brain is Data Science. Data Science is a story, an evolution of human brains, machines, and intuitions. To begin this story, what data scientists did was map the behavior of guessing with the basics of mathematics.

Regularization is a technique to solve the problem of overfitting in a machine learning algorithm by penalizing the cost function. It does so by using an additional penalty term in the cost function. So, how can L2 Regularization help to prevent overfitting? Let's first look at our new cost function: It controls the trade-off between two goals: fitting the training data well vs keeping the params small to avoid overfitting. The regularization term will heavily penalize large wᵢ.

Tsetlin Machines (TMs) capture patterns using conjunctive clauses in propositional logic, thus facilitating interpretation. However, recent TM-based approaches mainly rely on inspecting the full range of clauses individually. Such inspection does not necessarily scale to complex prediction problems that require a large number of clauses. In this paper, we propose closed-form expressions for understanding why a TM model makes a specific prediction (local interpretability). Additionally, the expressions capture the most important features of the model overall (global interpretability). We further introduce expressions for measuring the importance of feature value ranges for continuous features. The expressions are formulated directly from the conjunctive clauses of the TM, making it possible to capture the role of features in real-time, also during the learning process as the model evolves. Additionally, from the closed-form expressions, we derive a novel data clustering algorithm for visualizing high-dimensional data in three dimensions. Finally, we compare our proposed approach against SHAP and state-of-the-art interpretable machine learning techniques. For both classification and regression, our evaluation show correspondence with SHAP as well as competitive prediction accuracy in comparison with XGBoost, Explainable Boosting Machines, and Neural Additive Models.

The classical approach to non-linear regression in physics, is to take a mathematical model describing the functional dependence of the dependent variable from a set of independent variables, and then, using non-linear fitting algorithms, extract the parameters used in the modeling. Particularly challenging are real systems, characterized by several additional influencing factors related to specific components, like electronics or optical parts. In such cases, to make the model reproduce the data, empirically determined terms are built-in the models to compensate for the impossibility of modeling things that are, by construction, impossible to model. A new approach to solve this issue is to use neural networks, particularly feed-forward architectures with a sufficient number of hidden layers and an appropriate number of output neurons, each responsible for predicting the desired variables. Unfortunately, feed-forward neural networks (FFNNs) usually perform less efficiently when applied to multi-dimensional regression problems, that is when they are required to predict simultaneously multiple variables that depend from the input dataset in fundamentally different ways. To address this problem, we propose multi-task learning (MTL) architectures. These are characterized by multiple branches of task-specific layers, which have as input the output of a common set of layers. To demonstrate the power of this approach for multi-dimensional regression, the method is applied to luminescence sensing. Here the MTL architecture allows predicting multiple parameters, the oxygen concentration and the temperature, from a single set of measurements.

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Online Courses Udemy - Deep Learning Prerequisites: Linear Regression in Python, Data science: Learn linear regression from scratch and build your own working program in Python for data analysis. Bestseller Created by Lazy Programmer Inc English [Auto], Spanish [Auto] Students also bought Recommender Systems and Deep Learning in Python Unsupervised Deep Learning in Python Machine Learning and AI: Support Vector Machines in Python Data Science: Natural Language Processing (NLP) in Python Natural Language Processing with Deep Learning in Python Ensemble Machine Learning in Python: Random Forest, AdaBoost Preview this course GET COUPON CODE Description This course teaches you about one popular technique used in machine learning, data science and statistics: linear regression. We cover the theory from the ground up: derivation of the solution, and applications to real-world problems. We show you how one might code their own linear regression module in Python. Linear regression is the simplest machine learning model you can learn, yet there is so much depth that you'll be returning to it for years to come.

Principal Component Analysis (PCA) is a powerful and well-established data transformation method that can be used for data visualization, dimensionality reduction, and possibly improved performance with supervised learning tasks. In this use case blog, we examine a dataset consisting of measurements of benign and malignant tumors which are computed from digital images of a fine needle aspirate of breast mass tissue. Specifically, these 30 variables describe specific characteristics of the cell nuclei present in the images, such as texture symmetry and radius. The first step in applying PCA to this process was to see if we can more easily visualize separation between the malignant and benign classes in two dimensions. To do this, we first divide our dataset into train and test sets and perform the PCA using only the training data.

Kernel survival analysis methods predict subject-specific survival curves and times using information about which training subjects are most similar to a test subject. These most similar training subjects could serve as forecast evidence. How similar any two subjects are is given by the kernel function. In this paper, we present the first neural network framework that learns which kernel functions to use in kernel survival analysis. We also show how to use kernel functions to construct prediction intervals of survival time estimates that are statistically valid for individuals similar to a test subject. These prediction intervals can use any kernel function, such as ones learned using our neural kernel learning framework or using random survival forests. Our experiments show that our neural kernel survival estimators are competitive with a variety of existing survival analysis methods, and that our prediction intervals can help compare different methods' uncertainties, even for estimators that do not use kernels. In particular, these prediction interval widths can be used as a new performance metric for survival analysis methods.

Predicting COVID-19 in India using Machine Learning.In this session, we will take a COVID-19 dataset and understand how the disease has spread across different states in India. We will perform some data manipulation and data visualization operations on top of the dataset. Great Learning brings you this live session on'Predicting COVID-19 in India using Machine Learning'.In this session, we will take a COVID-19 dataset and understand how the disease has spread across different states in India. We will perform some data manipulation and data visualization operations on top of the dataset.