We consider the problem of recovering low-rank matrices from random rank-one measurements, which spans numerous applications including covariance sketching, phase retrieval, quantum state tomography, and learning shallow polynomial neural networks, among others. Our approach is to directly estimate the low-rank factor by minimizing a nonconvex quadratic loss function via vanilla gradient descent, following a tailored spectral initialization. When the true rank is small, this algorithm is guaranteed to converge to the ground truth (up to global ambiguity) with near-optimal sample complexity and computational complexity. To the best of our knowledge, this is the first guarantee that achieves near-optimality in both metrics. In particular, the key enabler of near-optimal computational guarantees is an implicit regularization phenomenon: without explicit regularization, both spectral initialization and the gradient descent iterates automatically stay within a region incoherent with the measurement vectors. This feature allows one to employ much more aggressive step sizes compared with the ones suggested in prior literature, without the need of sample splitting.

High-dimensional settings, where the data dimension ($d$) far exceeds the number of observations ($n$), are common in many statistical and machine learning applications. Methods based on $\ell_1$-relaxation, such as Lasso, are very popular for sparse recovery in these settings. Restricted Eigenvalue (RE) condition is among the weakest, and hence the most general, condition in literature imposed on the Gram matrix that guarantees nice statistical properties for the Lasso estimator. It is natural to ask: what families of matrices satisfy the RE condition? Following a line of work in this area, we construct a new broad ensemble of dependent random design matrices that have an explicit RE bound. Our construction starts with a fixed (deterministic) matrix $X \in \mathbb{R}^{n \times d}$ satisfying a simple stable rank condition, and we show that a matrix drawn from the distribution $X \Phi^\top \Phi$, where $\Phi \in \mathbb{R}^{m \times d}$ is a subgaussian random matrix, with high probability, satisfies the RE condition. This construction allows incorporating a fixed matrix that has an easily {\em verifiable} condition into the design process, and allows for generation of {\em compressed} design matrices that have a lower storage requirement than a standard design matrix. We give two applications of this construction to sparse linear regression problems, including one to a compressed sparse regression setting where the regression algorithm only has access to a compressed representation of a fixed design matrix $X$.

Vehicle recognition and classification have broad applications, ranging from traffic flow management to military target identification. We demonstrate an unsupervised method for automated identification of moving vehicles from roadside audio sensors. Using a short-time Fourier transform to decompose audio signals, we treat the frequency signature in each time window as an individual data point. We then use a spectral embedding for dimensionality reduction. Based on the leading eigenvectors, we relate the performance of an incremental reseeding algorithm to that of spectral clustering. We find that incremental reseeding accurately identifies individual vehicles using their acoustic signatures.

We extend conformal inference to general settings that allow for time series data. Our proposal is developed as a randomization method and accounts for potential serial dependence by including block structures in the permutation scheme. As a result, the proposed method retains the exact, model-free validity when the data are i.i.d. or more generally exchangeable, similar to usual conformal inference methods. When exchangeability fails, as is the case for common time series data, the proposed approach is approximately valid under weak assumptions on the conformity score.

Multi-armed bandit (MAB) is a class of online learning problems where a learning agent aims to maximize its expected cumulative reward while repeatedly selecting to pull arms with unknown reward distributions. In this paper, we consider a scenario in which the arms' reward distributions may change in a piecewise-stationary fashion at unknown time steps. By connecting change-detection techniques with classic UCB algorithms, we motivate and propose a learning algorithm called M-UCB, which can detect and adapt to changes, for the considered scenario. We also establish an $O(\sqrt{MKT\log T})$ regret bound for M-UCB, where $T$ is the number of time steps, $K$ is the number of arms, and $M$ is the number of stationary segments. Comparison with the best available lower bound shows that M-UCB is nearly optimal in $T$ up to a logarithmic factor. We also compare M-UCB with state-of-the-art algorithms in a numerical experiment based on a public Yahoo! dataset. In this experiment, M-UCB achieves about $50 \%$ regret reduction with respect to the best performing state-of-the-art algorithm.

The LU decomposition is found using an iterative numerical process and can fail for those matrices that cannot be decomposed or decomposed easily. A variation of this decomposition that is numerically more stable to solve in practice is called the LUP decomposition, or the LU decomposition with partial pivoting. The rows of the parent matrix are re-ordered to simplify the decomposition process and the additional P matrix specifies a way to permute the result or return the result to the original order. There are also other variations of the LU. The LU decomposition is often used to simplify the solving of systems of linear equations, such as finding the coefficients in a linear regression, as well as in calculating the determinant and inverse of a matrix.

Prerequisites: No prerequisites, knowledge of some undergraduate level mathematics would help but is not mandatory. Working knowledge of Python would be helpful if you want to run the source code that is provided. Taught by a Stanford-educated, ex-Googler and an IIT, IIM – educated ex-Flipkart lead analyst. This team has decades of practical experience in quant trading, analytics and e-commerce. The course is shy but confident: It is authoritative, drawn from decades of practical experience -but shies away from needlessly complicating stuff.

In the age where machines are learning to work like humans the advancements have gone far ahead, Our Speaker Dr Prashant is working on allowing machines to read the most difficult aspect in the field of medicine that is to read X-rays, scans and MRI's. Watch him share his idea here. Dr Prashant Warier is CEO, Qure.ai & Chief Data Scientist, Fractal Analytics with 16 years of experience in architecting and developing data science solutions. Prashant founded AI-powered personalized digital marketing firm Imagna Analytics which was acquired by Fractal in 2015. Earlier, he worked with SAP and was instrumental in building their Data Science practice.

Say, you appeared for the position of Statistical analyst at WalmartLabs. Now like most of the companies, you don't just have one round of interview. You have multiple rounds of interviews. Each one of these interviews is chaired by independent panels. Generally, even the questions asked in these interviews differ from each other.

Then we print out the version of TensorFlow we are using. We are using TensorFlow 1.0.1. We import NumPy as np. Then we print out the version of NumPy we are using. We are using NumPy 1.13.3.