During the 21st century, the revolution in data storage techniques reduces the storage cost of the data as a result the amount of data generated is growing exponentially. It is estimated the by the end of the 21st we will have 44 zettabytes of data. Every action we perform generates data viz. The algorithm we are using such as Naïve Bayes, KNN clustering, etc. has roots back in the 1960s but due to the technology barrier was not able to implement this algorithm. But in the 21st-century lot of innovation has been taken place -- result hardware has been evolved.

Some people call this artificial intelligence, but the reality is this technology will enhance us. So instead of artificial intelligence, I think we'll augment our intelligence." Every species survive on the basis of the type of intelligence they possess. Homo Sapiens are termed as the most "intelligent" species of all because their intelligence consists of many additional and more advanced qualities as compared to others. Now, when a machine is made or taught to mimic the human tendency to fulfill the above five qualities of intelligence, it is termed as Artificial Intelligence.

The predict function in Python is Y X * Beta, where Y is a column vector, X is the design matrix, and Beta is the column vector of parameters. You could definitely programmatically create the equation in the form that you want though. I don't what function/module you are using for your regression. Are you processing the data into polynomial features, then feeding that to a linear regression model? In this PolynomialFeatures preprocessing class, you can use the .get_feature_names()

If we look at the p-values of some of the variables, the values seem to be pretty high, which means they aren't significant. That means we can drop those variables from the model. Before dropping the variables, as discussed above, we have to see the multicollinearity between the variables. We do that by calculating the VIF value. Variance Inflation Factor or VIF is a quantitative value that says how much the feature variables are correlated with each other. It is an extremely important parameter to test our linear model.

Imbalanced learning (IL), i.e., learning unbiased models from class-imbalanced data, is a challenging problem. Typical IL methods including resampling and reweighting were designed based on some heuristic assumptions. They often suffer from unstable performance, poor applicability, and high computational cost in complex tasks where their assumptions do not hold. In this paper, we introduce a novel ensemble IL framework named MESA. It adaptively resamples the training set in iterations to get multiple classifiers and forms a cascade ensemble model. MESA directly learns the sampling strategy from data to optimize the final metric beyond following random heuristics. Moreover, unlike prevailing meta-learning-based IL solutions, we decouple the model-training and meta-training in MESA by independently train the meta-sampler over task-agnostic meta-data. This makes MESA generally applicable to most of the existing learning models and the meta-sampler can be efficiently applied to new tasks. Extensive experiments on both synthetic and real-world tasks demonstrate the effectiveness, robustness, and transferability of MESA. Our code is available at https://github.com/ZhiningLiu1998/mesa.

The thesis explores the role machine learning methods play in creating intuitive computational models of neural processing. Combined with interpretability techniques, machine learning could replace human modeler and shift the focus of human effort to extracting the knowledge from the ready-made models and articulating that knowledge into intuitive descroptions of reality. This perspective makes the case in favor of the larger role that exploratory and data-driven approach to computational neuroscience could play while coexisting alongside the traditional hypothesis-driven approach. We exemplify the proposed approach in the context of the knowledge representation taxonomy with three research projects that employ interpretability techniques on top of machine learning methods at three different levels of neural organization. The first study (Chapter 3) explores feature importance analysis of a random forest decoder trained on intracerebral recordings from 100 human subjects to identify spectrotemporal signatures that characterize local neural activity during the task of visual categorization. The second study (Chapter 4) employs representation similarity analysis to compare the neural responses of the areas along the ventral stream with the activations of the layers of a deep convolutional neural network. The third study (Chapter 5) proposes a method that allows test subjects to visually explore the state representation of their neural signal in real time. This is achieved by using a topology-preserving dimensionality reduction technique that allows to transform the neural data from the multidimensional representation used by the computer into a two-dimensional representation a human can grasp. The approach, the taxonomy, and the examples, present a strong case for the applicability of machine learning methods to automatic knowledge discovery in neuroscience.

Contrastive representation learning has shown to be an effective way of learning representations from unlabeled data. However, much progress has been made in vision domains relying on data augmentations carefully designed using domain knowledge. In this work, we propose i-Mix, a simple yet effective regularization strategy for improving contrastive representation learning in both vision and non-vision domains. We cast contrastive learning as training a non-parametric classifier by assigning a unique virtual class to each data in a batch. Then, data instances are mixed in both the input and virtual label spaces, providing more augmented data during training. In experiments, we demonstrate that i-Mix consistently improves the quality of self-supervised representations across domains, resulting in significant performance gains on downstream tasks. Furthermore, we confirm its regularization effect via extensive ablation studies across model and dataset sizes.

Distributed Gaussian processes (DGPs) are prominent local approximation methods to scale Gaussian processes (GPs) to large datasets. Instead of a global estimation, they train local experts by dividing the training set into subsets, thus reducing the time complexity. This strategy is based on the conditional independence assumption, which basically means that there is a perfect diversity between the local experts. In practice, however, this assumption is often violated, and the aggregation of experts leads to sub-optimal and inconsistent solutions. In this paper, we propose a novel approach for aggregating the Gaussian experts by detecting strong violations of conditional independence. The dependency between experts is determined by using a Gaussian graphical model, which yields the precision matrix. The precision matrix encodes conditional dependencies between experts and is used to detect strongly dependent experts and construct an improved aggregation. Using both synthetic and real datasets, our experimental evaluations illustrate that our new method outperforms other state-of-the-art (SOTA) DGP approaches while being substantially more time-efficient than SOTA approaches, which build on independent experts.

Making predictions that are fair with regard to protected group membership (race, gender, age, etc.) has become an important requirement for classification algorithms. Existing techniques derive a fair model from sampled labeled data relying on the assumption that training and testing data are identically and independently drawn (iid) from the same distribution.In practice, distribution shift can and does occur between training and testing datasets as the characteristics of individuals interacting with the machine learning system -- and which individuals interact with the system -- change. We investigate fairness under covariate shift, a relaxation of the iid assumption in which the inputs or covariates change while the conditional label distribution remains the same. We seek fair decisions under these assumptions on target data with unknown labels.We propose an approach that obtains the predictor that is robust to the worst-case in terms of target performance while satisfying target fairness requirements and matching statistical properties of the source data. We demonstrate the benefits of our approach on benchmark prediction tasks.

We propose a novel graph cross network (GXN) to achieve comprehensive feature learning from multiple scales of a graph. Based on trainable hierarchical representations of a graph, GXN enables the interchange of intermediate features across scales to promote information flow. Two key ingredients of GXN include a novel vertex infomax pooling (VIPool), which creates multiscale graphs in a trainable manner, and a novel feature-crossing layer, enabling feature interchange across scales. The proposed VIPool selects the most informative subset of vertices based on the neural estimation of mutual information between vertex features and neighborhood features. The intuition behind is that a vertex is informative when it can maximally reflect its neighboring information. The proposed feature-crossing layer fuses intermediate features between two scales for mutual enhancement by improving information flow and enriching multiscale features at hidden layers. The cross shape of the feature-crossing layer distinguishes GXN from many other multiscale architectures. Experimental results show that the proposed GXN improves the classification accuracy by 2.12% and 1.15% on average for graph classification and vertex classification, respectively. Based on the same network, the proposed VIPool consistently outperforms other graph-pooling methods.