How oversampling yielded great results for classifying cases of Sexual Harassment. When it comes to data science, sexual harassment is an imbalanced data problem, meaning there are few (known) instances of harassment in the entire dataset. An imbalanced problem is defined as a dataset which has disproportional class counts. Oversampling is one way to combat this by creating synthetic minority samples. SMOTE -- Synthetic Minority Over-sampling Technique -- is a common oversampling method widely used in machine learning with imbalanced high-dimensional datasets using Oversampling.

In my previous article, we analyzed the COVID-19 data of Turkey and selected the cubic model for predicting the spread of disease. In this article, we will show in detail why we selected the cubic model for prediction and see whether our decision was right or not. When we analyze the regression trend models we should consider overfitting and underfitting situations; underfitting indicates high bias and low variance while overfitting indicates low bias and high variance. The adjusted coefficient of determination is used in the different degrees of polynomial trend regression models comparing. When we examine the above formulas, we can notice the similarity between SSE and bias.

As machine learning is increasingly used in essential systems, it is important to reduce or eliminate the incidence of serious bugs. A growing body of research has developed machine learning algorithms with formal guarantees about performance, robustness, or fairness. Yet, the analysis of these algorithms is often complex, and implementing such systems in practice introduces room for error. Proof assistants can be used to formally verify machine learning systems by constructing machine checked proofs of correctness that rule out such bugs. However, reasoning about probabilistic claims inside of a proof assistant remains challenging. We show how a probabilistic program can be automatically represented in a theorem prover using the concept of \emph{reparameterization}, and how some of the tedious proofs of measurability can be generated automatically from the probabilistic program. To demonstrate that this approach is broad enough to handle rather different types of machine learning systems, we verify both a classic result from statistical learning theory (PAC-learnability of decision stumps) and prove that the null model used in a Bayesian hypothesis test satisfies a fairness criterion called demographic parity.

The inertial navigation system (INS) has been widely used to provide self-contained and continuous motion estimation in intelligent transportation systems. Recently, the emergence of chip-level inertial sensors has expanded the relevant applications from positioning, navigation, and mobile mapping to location-based services, unmanned systems, and transportation big data. Meanwhile, benefit from the emergence of big data and the improvement of algorithms and computing power, artificial intelligence (AI) has become a consensus tool that has been successfully applied in various fields. This article reviews the research on using AI technology to enhance inertial sensing from various aspects, including sensor design and selection, calibration and error modeling, navigation and motion-sensing algorithms, multi-sensor information fusion, system evaluation, and practical application. Based on the over 30 representative articles selected from the nearly 300 related publications, this article summarizes the state of the art, advantages, and challenges on each aspect. Finally, it summarizes nine advantages and nine challenges of AI-enhanced inertial sensing and then points out future research directions.

Density deconvolution is the task of estimating a probability density function given only noise-corrupted samples. We can fit a Gaussian mixture model to the underlying density by maximum likelihood if the noise is normally distributed, but would like to exploit the superior density estimation performance of normalizing flows and allow for arbitrary noise distributions. Since both adjustments lead to an intractable likelihood, we resort to amortized variational inference. We demonstrate some problems involved in this approach, however, experiments on real data demonstrate that flows can already out-perform Gaussian mixtures for density deconvolution.

A central question in many fields of scientific research is to determine how an outcome would be affected by an action, or to measure the effect of an action (a.k.a treatment effect). In recent years, a need for estimating the heterogeneous treatment effects conditioning on the different characteristics of individuals has emerged from research fields such as personalized healthcare, social science, and online marketing. To meet the need, researchers and practitioners from different communities have developed algorithms by taking the treatment effect heterogeneity modeling approach and the uplift modeling approach, respectively. In this paper, we provide a unified survey of these two seemingly disconnected yet closely related approaches under the potential outcome framework. We then provide a structured survey of existing methods by emphasizing on their inherent connections with a set of unified notations to make comparisons of the different methods easy. We then review the main applications of the surveyed methods in personalized marketing, personalized medicine, and social studies. Finally, we summarize the existing software packages and present discussions based on the use of methods on synthetic, semi-synthetic and real world data sets and provide some general guidelines for choosing methods.

We provide a detailed asymptotic study of gradient flow trajectories and their implicit optimization bias when minimizing the exponential loss over "diagonal linear networks". This is the simplest model displaying a transition between "kernel" and non-kernel ("rich" or "active") regimes. We show how the transition is controlled by the relationship between the initialization scale and how accurately we minimize the training loss. Our results indicate that some limit behaviors of gradient descent only kick in at ridiculous training accuracies (well beyond $10^{-100}$). Moreover, the implicit bias at reasonable initialization scales and training accuracies is more complex and not captured by these limits.

Deep learning currently provides the best representations of complex objects for a wide variety of tasks. However, learning these representations is an expensive process that requires very large training samples and significant computing resources. Thankfully, sharing these representations is a common practice, enabling to solve new tasks with relatively little training data and few computing resources; the transfer of representations is nowadays an essential ingredient in numerous real-world applications of deep learning. Transferring representations commonly relies on the parameterized form of the features making up the representation, as encoded by the computational graph of these features. In this paper, we propose to use a novel non-parametric metric between representations. It is based on a functional view of features, and takes into account certain invariances of representations, such as the permutation of their features, by relying on optimal transport. This distance is used as a regularization term promoting similarity between two representations. We show the relevance of this approach in two representation transfer settings, where the representation of a trained reference model is transferred to another one, for solving a new related task (inductive transfer learning), or for distilling knowledge to a simpler model (model compression).

Our understanding of learning input-output relationships with neural nets has improved rapidly in recent years, but little is known about the convergence of the underlying representations, even in the simple case of linear autoencoders (LAEs). We show that when trained with proper regularization, LAEs can directly learn the optimal representation -- ordered, axis-aligned principal components. We analyze two such regularization schemes: non-uniform $\ell_2$ regularization and a deterministic variant of nested dropout [Rippel et al, ICML' 2014]. Though both regularization schemes converge to the optimal representation, we show that this convergence is slow due to ill-conditioning that worsens with increasing latent dimension. We show that the inefficiency of learning the optimal representation is not inevitable -- we present a simple modification to the gradient descent update that greatly speeds up convergence empirically.

In this paper we study Lipschitz regularity of elliptic PDEs on geometric graphs, constructed from random data points. The data points are sampled from a distribution supported on a smooth manifold. The family of equations that we study arises in data analysis in the context of graph-based learning and contains, as important examples, the equations satisfied by graph Laplacian eigenvectors. In particular, we prove high probability interior and global Lipschitz estimates for solutions of graph Poisson equations. Our results can be used to show that graph Laplacian eigenvectors are, with high probability, essentially Lipschitz regular with constants depending explicitly on their corresponding eigenvalues. Our analysis relies on a probabilistic coupling argument of suitable random walks at the continuum level, and an interpolation method for extending functions on random point clouds to the continuum manifold. As a byproduct of our general regularity results, we obtain high probability $L^\infty$ and approximate $\mathcal{C}^{0,1}$ convergence rates for the convergence of graph Laplacian eigenvectors towards eigenfunctions of the corresponding weighted Laplace-Beltrami operators. The convergence rates we obtain scale like the $L^2$-convergence rates established by two of the authors in previous work.