Machine learning has achieved great success in many applications, including electroencephalogram (EEG) based brain-computer interfaces (BCIs). Unfortunately, many machine learning models are vulnerable to adversarial examples, which are crafted by adding deliberately designed perturbations to the original inputs. Many adversarial attack approaches for classification problems have been proposed, but few have considered target adversarial attacks for regression problems. This paper proposes two such approaches. More specifically, we consider white-box target attacks for regression problems, where we know all information about the regression model to be attacked, and want to design small perturbations to change the regression output by a pre-determined amount. Experiments on two BCI regression problems verified that both approaches are effective. Moreover, adversarial examples generated from both approaches are also transferable, which means that we can use adversarial examples generated from one known regression model to attack an unknown regression model, i.e., to perform black-box attacks. To our knowledge, this is the first study on adversarial attacks for EEG-based BCI regression problems, which calls for more attention on the security of BCI systems.

Eye tracking is handled as one of the key technologies for applications which assess and evaluate human attention, behavior and biometrics, especially using gaze, pupillary and blink behaviors. One of the main challenges with regard to the social acceptance of eye-tracking technology is however the preserving of sensitive and personal information. To tackle this challenge, we employed a privacy-preserving framework based on randomized encoding to train a Support Vector Regression model on synthetic eye images privately to estimate human gaze. During the computation, none of the parties learns about the data or the result that any other party has. Furthermore, the party that trains the model cannot reconstruct pupil, blink or visual scanpath. The experimental results showed that our privacy preserving framework is also capable of working in real-time, as accurate as a non-private version of it and could be extended to other eye-tracking related problems.

We investigate the computational complexity of several basic linear algebra primitives, including largest eigenvector computation and linear regression, in the computational model that allows access to the data via a matrix-vector product oracle. We show that for polynomial accuracy, $\Theta(d)$ calls to the oracle are necessary and sufficient even for a randomized algorithm. Our lower bound is based on a reduction to estimating the least eigenvalue of a random Wishart matrix. This simple distribution enables a concise proof, leveraging a few key properties of the random Wishart ensemble.

While model selection is a well-studied topic in parametric and nonparametric regression or density estimation, model selection of possibly high dimensional nuisance parameters in semiparametric problems is far less developed. In this paper, we propose a new model selection framework for making inferences about a finite dimensional functional defined on a semiparametric model, when the latter admits a doubly robust estimating function. The class of such doubly robust functionals is quite large, including many missing data and causal inference problems. Under double robustness, the estimated functional should incur no bias if either of two nuisance parameters is evaluated at the truth while the other spans a large collection of candidate models. We introduce two model selection criteria for bias reduction of functional of interest, each based on a novel definition of pseudo-risk for the functional that embodies this double robustness property and thus may be used to select the candidate model that is nearest to fulfilling this property even when all models are wrong. Both selection criteria have a bias awareness property that selection of one nuisance parameter can be made to compensate for excessive bias due to poor learning of the other nuisance parameter. We establish an oracle property for a multi-fold cross-validation version of the new model selection criteria which states that our empirical criteria perform nearly as well as an oracle with a priori knowledge of the pseudo-risk for each candidate model. We also describe a smooth approximation to the selection criteria which allows for valid post-selection inference. Finally, we perform model selection of a semiparametric estimator of average treatment effect given an ensemble of candidate machine learning methods to account for confounding in a study of right heart catheterization in the ICU of critically ill patients.

In the previous article, we studied Linear Regression. One thing that I believe is that if we can correlate anything with us or our life, there are greater chances of understanding the concept. So I will try to explain everything by relating it to humans.

The original article is no longer available. Similar (and more comprehensive) material is available below. You can access this material here.

The original article is no longer available. Similar (and more comprehensive) material is available below. You can access this material here.

Using ensemble methods for regression has been a large success in obtaining high-accuracy prediction. Examples are Bagging, Random forest, Boosting, BART (Bayesian additive regression tree), and their variants. In this paper, we propose a new perspective named variable grouping to enhance the predictive performance. The main idea is to seek for potential grouping of variables in such way that there is no nonlinear interaction term between variables of different groups. Given a sum-of-learner model, each learner will only be responsible for one group of variables, which would be more efficient in modeling nonlinear interactions. We propose a two-stage method named variable grouping based Bayesian additive regression tree (GBART) with a well-developed python package gbart available. The first stage is to search for potential interactions and an appropriate grouping of variables. The second stage is to build a final model based on the discovered groups. Experiments on synthetic and real data show that the proposed method can perform significantly better than classical approaches.

Despite outstanding contribution to the significant progress of Artificial Intelligence (AI), deep learning models remain mostly black boxes, which are extremely weak in explainability of the reasoning process and prediction results. Explainability is not only a gateway between AI and society but also a powerful tool to detect flaws in the model and biases in the data. Local Interpretable Model-agnostic Explanation (LIME) is a recent approach that uses a linear regression model to form a local explanation for the individual prediction result. However, being so restricted and usually oversimplifying the relationships, linear models fail in situations where nonlinear associations and interactions exist among features and prediction results. This paper proposes an extended Decision Tree-based LIME (TLIME) approach, which uses a decision tree model to form an interpretable representation that is locally faithful to the original model. The new approach can capture nonlinear interactions among features in the data and creates plausible explanations. Various experiments show that the TLIME explanation of multiple blackbox models can achieve more reliable performance in terms of understandability, fidelity, and efficiency.

Suppose by means of some analysis, we were to deduce that today's value of the DJIA Closing Price may turn out to be a good predictor of tomorrow's Closing Price. To test this theory, we will develop a linear regression model consisting of a single regression variable. This variable will be the time lagged value of the time series. Here are the first few rows of the modified Data Frame. Let's remove the first row to get rid of the NaN: Next let's create our training and test data sets: Plot the model's performance against the test data set: At first glance, this model's performance looks much better than what we got from the mean model.