Recently, the online car-hailing service, Didi, has emerged as a leader in the sharing economy. Used by passengers and drivers extensive, it becomes increasingly important for the car-hailing service providers to minimize the waiting time of passengers and optimize the vehicle utilization, thus to improve the overall user experience. Therefore, the supply-demand estimation is an indispensable ingredient of an efficient online car-hailing service. To improve the accuracy of the estimation results, we analyze the implicit relationships between the points of Interest (POI) and the supply-demand gap in this paper. The different categories of POIs have positive or negative effects on the estimation, we propose a POI selection scheme and incorporate it into XGBoost [1] to achieve more accurate estimation results. Our experiment demonstrates our method provides more accurate estimation results and more stable estimation results than the existing methods.

Despite recent development in methodology, community detection remains a challenging problem. Existing literature largely focuses on the standard setting where a network is learned using an observed adjacency matrix from a single data source. Constructing a shared network from multiple data sources is more challenging due to the heterogeneity across populations. Additionally, when a natural ordering on the nodes of interest arises, no existing method takes such information into account. Motivated by grouping the International classification of diseases, ninth revision, (ICD9) codes to represent clinically meaningful phenotypes, we propose a novel spectral clustering method that optimally combines multiple data sources while leveraging the prior ordering knowledge. The proposed method combines a banding step to encourage a desired moving average structure with a subsequent weighting step to maximize consensus across multiple sources. Its statistical performance is thoroughly studied under a multi-view stochastic block model. We also provide a simple rule of choosing weights in practice. The efficacy and robustness of the method is fully demonstrated through extensive simulations. Finally, we apply the method to the ICD9 coding system and yield a very insightful clustering structure by integrating information from a large claim database and two healthcare systems.

And yet even those investors who understand AI in general may not truly understand how AI fits into the world of investing and, even more, how it can be used to impact and potentially improve investment decisions. One of the most important things to understand is that the lines between technology and AI have blurred. Even within the Nasdaq-100, an index focused on technology, it can be challenging to distinguish which index members fall into which category. Are they technology companies, AI companies, or both? Amazon's use of its AI-driven Kiva robots has helped it to become the largest online retailer in the world.

With deep convolutional neural networks (CNN) introduced by [1] and [2], computer vision tasks and more specifically image classification have made huge improvements in the years following [3]. CNN performances benefit a lot from big collections of annotated images like [4] or [5]. They are trained by optimizing a loss function with gradient descents computed on random mini-batches according to [6]. The method called stochastic gradient descent (SGD) has proved to be very efficient to train neural networks in general. However current CNN structures are extremely deep like the 100 layers ResNet of [7] and contains a lot of parameters (around 60M for Alexnet [3] and 130M for vgg [8]). Those structures involve heavy gradient computation times making the training on big data-sets very slow. Computation on GPU accelerates the training but requires huge local memory caches. Nevertheless the mini-batch optimization seems suitable for distributing the training over several threads. Many methods have been proposed like 1 [9, 10], which propose to distribute the batches over different threads called workers that periodically exchange information via a central thread to synchronize their models.

The overall performance or expected excess risk of an iterative machine learning algorithm can be decomposed into training error and generalization error. While the former is controlled by its convergence analysis, the latter can be tightly handled by algorithmic stability. The machine learning community has a rich history investigating convergence and stability separately. However, the question about the trade-off between these two quantities remains open. In this paper, we show that for any iterative algorithm at any iteration, the overall performance is lower bounded by the minimax statistical error over an appropriately chosen loss function class. This implies an important trade-off between convergence and stability of the algorithm -- a faster converging algorithm has to be less stable, and vice versa. As a direct consequence of this fundamental tradeoff, new convergence lower bounds can be derived for classes of algorithms constrained with different stability bounds. In particular, when the loss function is convex (or strongly convex) and smooth, we discuss the stability upper bounds of gradient descent (GD) and stochastic gradient descent and their variants with decreasing step sizes. For Nesterov's accelerated gradient descent (NAG) and heavy ball method (HB), we provide stability upper bounds for the quadratic loss function. Applying existing stability upper bounds for the gradient methods in our trade-off framework, we obtain lower bounds matching the well-established convergence upper bounds up to constants for these algorithms and conjecture similar lower bounds for NAG and HB. Finally, we numerically demonstrate the tightness of our stability bounds in terms of exponents in the rate and also illustrate via a simulated logistic regression problem that our stability bounds reflect the generalization errors better than the simple uniform convergence bounds for GD and NAG.

Many modern applications deal with multi-label data, such as functional categorizations of genes, image labeling and text categorization. Classification of such data with a large number of labels and latent dependencies among them is a challenging task, and it becomes even more challenging when the data is received online and in chunks. Many of the current multi-label classification methods require a lot of time and memory, which make them infeasible for practical real-world applications. In this paper, we propose a fast linear label space dimension reduction method that transforms the labels into a reduced encoded space and trains models on the obtained pseudo labels. Additionally, it provides an analytical method to update the decoding matrix which maps the labels into the original space and is used during the test phase. Experimental results show the effectiveness of this approach in terms of running times and the prediction performance over different measures. Keywords: data stream classification, multi-label data, label compression 1. Introduction Standard classification is the task of assigning the correct class to previously unknown test instances based on training instances. Training data consist of a set of features and an associated target class or class label. Many modern data mining applications, however, need to deal with more than one label per instance.

This tutorial was written by Manish Saraswat. "The road to machine learning starts with Regression. If you are aspiring to become a data scientist, regression is the first algorithm you need to learnmaster. Not just to clear job interviews, but to solve real world problems. Till today, a lot of consultancy firms continue to use regression techniques at a larger scale to help their clients.

Logistic Regression is one of the most powerful classification methods within machine learning and can be used for a wide variety of tasks. Think of pre-policing or predictive analytics in health; it can be used to aid tuberculosis patients, aid breast cancer diagnosis, etc. Think of modeling urban growth, analysing mortgage pre-payments and defaults, forecasting the direction and strength of stock market movement, and even predicting sport outcomes. Reading all of this, the theory[1] of Maximum Entropy Classification might look difficult. In my experience, the average Developer does not believe they can design a proper Maximum Entropy / Logistic Regression Classifier from scratch. I strongly disagree: not only is the mathematics behind is relatively simple, it can also be implemented with a few lines of code.

We prove a \emph{query complexity} lower bound for approximating the top $r$ dimensional eigenspace of a matrix. We consider an oracle model where, given a symmetric matrix $\mathbf{M} \in \mathbb{R}^{d \times d}$, an algorithm $\mathsf{Alg}$ is allowed to make $\mathsf{T}$ exact queries of the form $\mathsf{w}^{(i)} = \mathbf{M} \mathsf{v}^{(i)}$ for $i$ in $\{1,...,\mathsf{T}\}$, where $\mathsf{v}^{(i)}$ is drawn from a distribution which depends arbitrarily on the past queries and measurements $\{\mathsf{v}^{(j)},\mathsf{w}^{(i)}\}_{1 \le j \le i-1}$. We show that for every $\mathtt{gap} \in (0,1/2]$, there exists a distribution over matrices $\mathbf{M}$ for which 1) $\mathrm{gap}_r(\mathbf{M}) = \Omega(\mathtt{gap})$ (where $\mathrm{gap}_r(\mathbf{M})$ is the normalized gap between the $r$ and $r+1$-st largest-magnitude eigenvector of $\mathbf{M}$), and 2) any algorithm $\mathsf{Alg}$ which takes fewer than $\mathrm{const} \times \frac{r \log d}{\sqrt{\mathtt{gap}}}$ queries fails (with overwhelming probability) to identity a matrix $\widehat{\mathsf{V}} \in \mathbb{R}^{d \times r}$ with orthonormal columns for which $\langle \widehat{\mathsf{V}}, \mathbf{M} \widehat{\mathsf{V}}\rangle \ge (1 - \mathrm{const} \times \mathtt{gap})\sum_{i=1}^r \lambda_i(\mathbf{M})$. Our bound requires only that $d$ is a small polynomial in $1/\mathtt{gap}$ and $r$, and matches the upper bounds of Musco and Musco '15. Moreover, it establishes a strict separation between convex optimization and \emph{randomized}, "strict-saddle" non-convex optimization of which PCA is a canonical example: in the former, first-order methods can have dimension-free iteration complexity, whereas in PCA, the iteration complexity of gradient-based methods must necessarily grow with the dimension.

The interconnected nature of graphs often results in difficult to interpret clutter. Typically techniques focus on either decluttering by clustering nodes with similar properties or grouping edges with similar relationship. We propose using mapper, a powerful topological data analysis tool, to summarize the structure of a graph in a way that both clusters data with similar properties and preserves relationships. Typically, mapper operates on a given data by utilizing a scalar function defined on every point in the data and a cover for scalar function codomain. The output of mapper is a graph that summarize the shape of the space. In this paper, we outline how to use this mapper construction on an input graphs, outline three filter functions that capture important structures of the input graph, and provide an interface for interactively modifying the cover. To validate our approach, we conduct several case studies on synthetic and real world data sets and demonstrate how our method can give meaningful summaries for graphs with various complexities