We study the first gradient descent step on the first-layer parameters $\boldsymbol{W}$ in a two-layer neural network: $f(\boldsymbol{x}) = \frac{1}{\sqrt{N}}\boldsymbol{a}^\top\sigma(\boldsymbol{W}^\top\boldsymbol{x})$, where $\boldsymbol{W}\in\mathbb{R}^{d\times N}, \boldsymbol{a}\in\mathbb{R}^{N}$ are randomly initialized, and the training objective is the empirical MSE loss: $\frac{1}{n}\sum_{i=1}^n (f(\boldsymbol{x}_i)-y_i)^2$. In the proportional asymptotic limit where $n,d,N\to\infty$ at the same rate, and an idealized student-teacher setting, we show that the first gradient update contains a rank-1 "spike", which results in an alignment between the first-layer weights and the linear component of the teacher model $f^*$. To characterize the impact of this alignment, we compute the prediction risk of ridge regression on the conjugate kernel after one gradient step on $\boldsymbol{W}$ with learning rate $\eta$, when $f^*$ is a single-index model. We consider two scalings of the first step learning rate $\eta$. For small $\eta$, we establish a Gaussian equivalence property for the trained feature map, and prove that the learned kernel improves upon the initial random features model, but cannot defeat the best linear model on the input. Whereas for sufficiently large $\eta$, we prove that for certain $f^*$, the same ridge estimator on trained features can go beyond this "linear regime" and outperform a wide range of random features and rotationally invariant kernels. Our results demonstrate that even one gradient step can lead to a considerable advantage over random features, and highlight the role of learning rate scaling in the initial phase of training.

The Partial Least Square Regression (PLSR) exhibits admirable competence for predicting continuous variables from inter-correlated brain recordings in the brain-computer interface. However, PLSR is in essence formulated based on the least square criterion, thus, being non-robust with respect to noises. The aim of this study is to propose a new robust implementation for PLSR. To this end, the maximum correntropy criterion (MCC) is used to propose a new robust variant of PLSR, called as Partial Maximum Correntropy Regression (PMCR). The half-quadratic optimization is utilized to calculate the robust projectors for the dimensionality reduction, and the regression coefficients are optimized by a fixed-point approach. We evaluate the proposed PMCR with a synthetic example and the public Neurotycho electrocorticography (ECoG) datasets. The extensive experimental results demonstrate that, the proposed PMCR can achieve better prediction performance than the conventional PLSR and existing variants with three different performance indicators in high-dimensional and noisy regression tasks. PMCR can suppress the performance degradation caused by the adverse noise, ameliorating the decoding robustness of the brain-computer interface.

Machine Learning with AWS is the right place to start if you are a beginner interested in learning useful artificial intelligence (AI) and machine learning skills using Amazon Web Services (AWS), the most popular and powerful cloud platform. You will learn how to use AWS to transform your projects into apps that work at high speed and are highly scalable. From natural language processing (NLP) applications, such as language translation and understanding news articles and other text sources, to creating chatbots with both voice and text interfaces, you will learn all that there is to know about using AWS to your advantage. You will also understand how to process huge numbers of images fast and create machine learning models. By the end of this course, you will have developed the skills you need to efficiently use AWS in your machine learning and artificial intelligence projects.

By supporting this project, you contribute to global peace. In a world increasingly globalized, we must protect preserve, restore and safeguard the cultural heritage we inherited from our ancestors. Nurturing cultural diversity as a driving factor of peace creates spaces of dialogue to combat violence and oppression. For each backer token, you receive 0.3% ownership which is 0.3 % of sales fees for each sale in this collection. Aishatu's audio fiction will incorporate immersive sound design and original instrumental music.

A visit to DMart or Reliance Retail in India on any given day would make one think about Black Friday sales. The limited manpower in stores often falls short to tend to the swarm of shoppers in Indian retail stores. To solve the issue, Scribble Data strives to provide automated and customised solutions for retail businesses to tend to the demand and needs of every customer that walks in through their door. The startup offers retail chains real-time inventory management, identifies customer shopping trends, and provides personalised recommendations. Scribble Data helps businesses build machine learning (ML) applications for making their daily operations hassle free and for creating more market-worthy ML features.

In this paper, we consider the problem of making distributionally robust, skeptical inferences for the multi-label problem, or more generally for Boolean vectors. By distributionally robust, we mean that we consider a set of possible probability distributions, and by skeptical we understand that we consider as valid only those inferences that are true for every distribution within this set. Such inferences will provide partial predictions whenever the considered set is sufficiently big. We study in particular the Hamming loss case, a common loss function in multi-label problems, showing how skeptical inferences can be made in this setting. Our experimental results are organised in three sections; (1) the first one indicates the gain computational obtained from our theoretical results by using synthetical data sets, (2) the second one indicates that our approaches produce relevant cautiousness on those hard-to-predict instances where its precise counterpart fails, and (3) the last one demonstrates experimentally how our approach copes with imperfect information (generated by a downsampling procedure) better than the partial abstention [31] and the rejection rules.

Electronic address: mike.landry@hvl.no. 2 Western Norway University of Applied Sciences, Norway.

First, the IoT provides a platform that allows public-health agencies access to data for monitoring the COVID-19 pandemic. For example, the'Worldometer' provides a real-time update on the actual number of people known to have COVID-19 worldwide, including daily new cases of the disease, disease distribution by countries and severity of disease (recovered, critical condition or death) (https://www.worldometers.info/coronavirus/). Second, big data also provides opportunities for performing modeling studies of viral activity and for guiding individual country healthcare policymakers to enhance preparation for the outbreak. Using three global databases―the Official Aviation Guide, the location-based services of the Tencent (Shenzhen, China), and the Wuhan Municipal Transportation Management Bureau―Wu et al. performed a modeled study of'nowcasting' and forecasting COVID-19 disease activity within and outside China that could be used by the health authorities for public-health planning and control worldwide8. Similarly, using the WHO International Health Regulations, the State Parties Self-Assessment Annual Reporting Tool, Joint External Evaluation reports and the Infectious Disease Vulnerability Index, Gilbert et al. assessed the preparedness and vulnerability of African countries in battling against COVID-19; this would help raise awareness of the respective health authorities in Africa to better prepare for the viral outbreak9.

One of the most promising applications of quantum computing is the processing of graphical data like images. Here, we investigate the possibility of realizing a quantum pattern recognition protocol based on swap test, and use the IBMQ noisy intermediate-scale quantum (NISQ) devices to verify the idea. We find that with a two-qubit protocol, swap test can efficiently detect the similarity between two patterns with good fidelity, though for three or more qubits the noise in the real devices becomes detrimental. To mitigate this noise effect, we resort to destructive swap test, which shows an improved performance for three-qubit states. Due to limited cloud access to larger IBMQ processors, we take a segment-wise approach to apply the destructive swap test on higher dimensional images. In this case, we define an average overlap measure which shows faithfulness to distinguish between two very different or very similar patterns when simulated on real IBMQ processors. As test images, we use binary images with simple patterns, greyscale MNIST numbers and MNIST fashion images, as well as binary images of human blood vessel obtained from magnetic resonance imaging (MRI). We also present an experimental set up for applying destructive swap test using the nitrogen vacancy centre (NVs) in diamond. Our experimental data show high fidelity for single qubit states. Lastly, we propose a protocol inspired from quantum associative memory, which works in an analogous way to supervised learning for performing quantum pattern recognition using destructive swap test.

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