In real word applications, data generating process for training a machine learning model often differs from what the model encounters in the test stage. Understanding how and whether machine learning models generalize under such distributional shifts have been a theoretical challenge. Here, we study generalization in kernel regression when the training and test distributions are different using methods from statistical physics. Using the replica method, we derive an analytical formula for the out-of-distribution generalization error applicable to any kernel and real datasets. We identify an overlap matrix that quantifies the mismatch between distributions for a given kernel as a key determinant of generalization performance under distribution shift. Using our analytical expressions we elucidate various generalization phenomena including possible improvement in generalization when there is a mismatch. We develop procedures for optimizing training and test distributions for a given data budget to find best and worst case generalizations under the shift. We present applications of our theory to real and synthetic datasets and for many kernels. We compare results of our theory applied to Neural Tangent Kernel with simulations of wide networks and show agreement. We analyze linear regression in further depth.

Peacefulness is a principal dimension of well-being for all humankind and is the way out of inequity and every single form of violence. Thus, its measurement has lately drawn the attention of researchers and policy-makers. During the last years, novel digital data streams have drastically changed the research in this field. In the current study, we exploit information extracted from Global Data on Events, Location, and Tone (GDELT) digital news database, to capture peacefulness through the Global Peace Index (GPI). Applying predictive machine learning models, we demonstrate that news media attention from GDELT can be used as a proxy for measuring GPI at a monthly level. Additionally, we use the SHAP methodology to obtain the most important variables that drive the predictions. This analysis highlights each country's profile and provides explanations for the predictions overall, and particularly for the errors and the events that drive these errors. We believe that digital data exploited by Social Good researchers, policy-makers, and peace-builders, with data science tools as powerful as machine learning, could contribute to maximize the societal benefits and minimize the risks to peacefulness.

Linear regression is a fundamental modeling tool in statistics and related fields. In this paper, we study an important variant of linear regression in which the predictor-response pairs are partially mismatched. We use an optimization formulation to simultaneously learn the underlying regression coefficients and the permutation corresponding to the mismatches. The combinatorial structure of the problem leads to computational challenges. We propose and study a simple greedy local search algorithm for this optimization problem that enjoys strong theoretical guarantees and appealing computational performance. We prove that under a suitable scaling of the number of mismatched pairs compared to the number of samples and features, and certain assumptions on problem data; our local search algorithm converges to a nearly-optimal solution at a linear rate. In particular, in the noiseless case, our algorithm converges to the global optimal solution with a linear convergence rate. We also propose an approximate local search step that allows us to scale our approach to much larger instances. We conduct numerical experiments to gather further insights into our theoretical results and show promising performance gains compared to existing approaches.

In this new series, I took it upon myself to improve my coding skills and habits by writing clean, reusable, well-documented code with test cases. This is the first part of the series where I implement Linear, Polynomial, Ridge, Lasso, and ElasticNet Regression from scratch in an object-oriented manner. We'll start with a simple LinearRegression class and then build upon it creating an entire module of linear models in a simple style similar to Scikit-Learn. My implementations are in no way optimal solutions and are only meant to increase our understanding of machine learning. In the repository you will find all of the code found in this blog and more including test cases for every class and function.

Linear Algebra is a branch of mathematics that is extremely useful in data science and machine learning. Linear algebra is the most important math skill in machine learning. Most machine learning models can be expressed in matrix form. A dataset itself is often represented as a matrix. Linear algebra is used in data preprocessing, data transformation, and model evaluation.

Providing meaningful and actionable explanations to end-users is a fundamental prerequisite for implementing explainable intelligent systems in the real world. Explainability is a situated interaction between a user and the AI system rather than being static design principles. The content of explanations is context-dependent and must be defined by evidence about the user and its context. This paper seeks to operationalize this concept by proposing a formative architecture that defines the explanation space from a user-inspired perspective. The architecture comprises five intertwined components to outline explanation requirements for a task: (1) the end-users mental models, (2) the end-users cognitive process, (3) the user interface, (4) the human-explainer agent, and the (5) agent process. We first define each component of the architecture. Then we present the Abstracted Explanation Space, a modeling tool that aggregates the architecture's components to support designers in systematically aligning explanations with the end-users work practices, needs, and goals. It guides the specifications of what needs to be explained (content - end-users mental model), why this explanation is necessary (context - end-users cognitive process), to delimit how to explain it (format - human-explainer agent and user interface), and when should the explanations be given. We then exemplify the tool's use in an ongoing case study in the aircraft maintenance domain. Finally, we discuss possible contributions of the tool, known limitations/areas for improvement, and future work to be done.

We develop a distribution-free, unsupervised anomaly detection method called ECAD, which wraps around any regression algorithm and sequentially detects anomalies. Rooted in conformal prediction, ECAD does not require data exchangeability but approximately controls the Type-I error when data are normal. Computationally, it involves no data-splitting and efficiently trains ensemble predictors to increase statistical power. We demonstrate the superior performance of ECAD on detecting anomalous spatio-temporal traffic flow.

S{\o}gaard (2020) obtained results suggesting the fraction of trees occurring in the test data isomorphic to trees in the training set accounts for a non-trivial variation in parser performance. Similar to other statistical analyses in NLP, the results were based on evaluating linear regressions. However, the study had methodological issues and was undertaken using a small sample size leading to unreliable results. We present a replication study in which we also bin sentences by length and find that only a small subset of sentences vary in performance with respect to graph isomorphism. Further, the correlation observed between parser performance and graph isomorphism in the wild disappears when controlling for covariants. However, in a controlled experiment, where covariants are kept fixed, we do observe a strong correlation. We suggest that conclusions drawn from statistical analyses like this need to be tempered and that controlled experiments can complement them by more readily teasing factors apart.

Generalized Linear Model (GLiM, or GLM) is an advanced statistical modelling technique formulated by John Nelder and Robert Wedderburn in 1972. It is an umbrella term that encompasses many other models, which allows the response variable y to have an error distribution other than a normal distribution. The models include Linear Regression, Logistic Regression, and Poisson Regression. The underlying relationship between the response and the predictors is linear (i.e. Also, the error distribution of the response variable should be normally distributed.

Are you a working professional and looking for the best advanced data science courses? If yes, then you are in the right place. In this article, you will find the 7 Best Data Science Courses for Working Professionals. To gain data science skills, there are numerous courses available. So, without wasting your time, let's start finding the Best Data Science Courses for Working Professionals– This is a Nano-Degree Program offered by Udacity.