A.1 Algorithms We provide algorithms to describe the algorithmic contributions in the main paper.

Ridge estimation is an important manifold learning technique. The goal of this paper is to examine the effects of nonlinear transformations on the ridge sets. The main result proves the inclusion relationship between ridges: $\cR(f\circ p)\subseteq \cR(p)$, provided that the transformation $f$ is strictly increasing and concave on the range of the function $p$. Additionally, given an underlying true manifold $\cM$, we show that the Hausdorff distance between $\cR(f\circ p)$ and its projection onto $\cM$ is smaller than the Hausdorff distance between $\cR(p)$ and the corresponding projection. This motivates us to apply an increasing and concave transformation before the ridge estimation. In specific, we show that the power transformations $f^{q}(y)=y^q/q,-\infty

Transducer is one of the mainstream frameworks for streaming speech recognition. There is a performance gap between the streaming and non-streaming transducer models due to limited context. To reduce this gap, an effective way is to ensure that their hidden and output distributions are consistent, which can be achieved by hierarchical knowledge distillation. However, it is difficult to ensure the distribution consistency simultaneously because the learning of the output distribution depends on the hidden one. In this paper, we propose an adaptive two-stage knowledge distillation method consisting of hidden layer learning and output layer learning. In the former stage, we learn hidden representation with full context by applying mean square error loss function. In the latter stage, we design a power transformation based adaptive smoothness method to learn stable output distribution. It achieved 19\% relative reduction in word error rate, and a faster response for the first token compared with the original streaming model in LibriSpeech corpus.

BetterUp, the human transformation company,announced it has launched BetterUp Sales Performance on Salesforce AppExchange, empowering customers to reach peak performance through dedicated professional sales coaching and measure the impact coaching is having on business outcomes including quota attainment, deal velocity, time to productivity, and more. "BetterUp's Sales Performance is a welcome addition to AppExchange as it powers transformation for customers by unlocking team performance across sales organizations" Integrated directly with Salesforce, BetterUp's Sales Performance is currently available on AppExchange. Additionally, BetterUp and Salesforce customers will soon have access to a dashboard embedded into Salesforce that measures revenue-related metrics driven by coaches and non-coached sales representatives. "Salesforce is one of the first adopters of the Human Transformation Platform and remains committed to the importance of mental fitness, inclusion and connection," said Alexi Robichaux, CEO and co-founder of BetterUp. "With our expanded partnership, sales managers and sellers using Sales Cloud will now have support to strategize on deals, prep for prospect calls, and develop the right mindsets around resilience, focus, and agility. We're thrilled to bring this solution to Salesforce customers to help them achieve and exceed sales performance."

Solar flares, especially the M- and X-class flares, are often associated with coronal mass ejections (CMEs). They are the most important sources of space weather effects, that can severely impact the near-Earth environment. Thus it is essential to forecast flares (especially the M-and X-class ones) to mitigate their destructive and hazardous consequences. Here, we introduce several statistical and Machine Learning approaches to the prediction of the AR's Flare Index (FI) that quantifies the flare productivity of an AR by taking into account the numbers of different class flares within a certain time interval. Specifically, our sample includes 563 ARs appeared on solar disk from May 2010 to Dec 2017. The 25 magnetic parameters, provided by the Space-weather HMI Active Region Patches (SHARP) from Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO), characterize coronal magnetic energy stored in ARs by proxy and are used as the predictors. We investigate the relationship between these SHARP parameters and the FI of ARs with a machine-learning algorithm (spline regression) and the resampling method (Synthetic Minority Over-Sampling Technique for Regression with Gaussian Noise, short by SMOGN). Based on the established relationship, we are able to predict the value of FIs for a given AR within the next 1-day period. Compared with other 4 popular machine learning algorithms, our methods improve the accuracy of FI prediction, especially for large FI. In addition, we sort the importance of SHARP parameters by Borda Count method calculated from the ranks that are rendered by 9 different machine learning methods.

We develop the "generalized consistent weighted sampling" (GCWS) for hashing the "powered-GMM" (pGMM) kernel (with a tuning parameter $p$). It turns out that GCWS provides a numerically stable scheme for applying power transformation on the original data, regardless of the magnitude of $p$ and the data. The power transformation is often effective for boosting the performance, in many cases considerably so. We feed the hashed data to neural networks on a variety of public classification datasets and name our method ``GCWSNet''. Our extensive experiments show that GCWSNet often improves the classification accuracy. Furthermore, it is evident from the experiments that GCWSNet converges substantially faster. In fact, GCWS often reaches a reasonable accuracy with merely (less than) one epoch of the training process. This property is much desired because many applications, such as advertisement click-through rate (CTR) prediction models, or data streams (i.e., data seen only once), often train just one epoch. Another beneficial side effect is that the computations of the first layer of the neural networks become additions instead of multiplications because the input data become binary (and highly sparse). Empirical comparisons with (normalized) random Fourier features (NRFF) are provided. We also propose to reduce the model size of GCWSNet by count-sketch and develop the theory for analyzing the impact of using count-sketch on the accuracy of GCWS. Our analysis shows that an ``8-bit'' strategy should work well in that we can always apply an 8-bit count-sketch hashing on the output of GCWS hashing without hurting the accuracy much. There are many other ways to take advantage of GCWS when training deep neural networks. For example, one can apply GCWS on the outputs of the last layer to boost the accuracy of trained deep neural networks.

The Simultaneous Localization and Mapping (SLAM) problem addresses the possibility of a robot to localize itself in an unknown environment and simultaneously build a consistent map of this environment. Recently, cameras have been successfully used to get the environment's features to perform SLAM, which is referred to as visual SLAM (VSLAM). However, classical VSLAM algorithms can be easily induced to fail when either the motion of the robot or the environment is too challenging. Although new approaches based on Deep Neural Networks (DNNs) have achieved promising results in VSLAM, they still are unable to outperform traditional methods. To leverage the robustness of deep learning to enhance traditional VSLAM systems, we propose to combine the potential of deep learning-based feature descriptors with the traditional geometry-based VSLAM, building a new VSLAM system called LIFT-SLAM. Experiments conducted on KITTI and Euroc datasets show that deep learning can be used to improve the performance of traditional VSLAM systems, as the proposed approach was able to achieve results comparable to the state-of-the-art while being robust to sensorial noise. We enhance the proposed VSLAM pipeline by avoiding parameter tuning for specific datasets with an adaptive approach while evaluating how transfer learning can affect the quality of the features extracted.

Numeric data is almost a blessing. Well, because it is already in a format that is ingestible by Machine Learning models. However, if we translate it into human-relatable terms, just because a PhD level textbook is written in English -- I speak, read and write in English -- does not mean that I am capable of understanding the textbook well enough to derive useful insights. What would make the textbook useful to me is if it epitomizes the most important information in a manner that considers the assumptions of my mental model, such as "Maths is a myth" (which, by the way, is no longer my view since I am really starting to enjoying it). In the same way, a good feature should represent salient aspects of the data, as well as taking the shape of the assumptions that are made by the Machine Learning model.

I created a custom'particle optimizer' and published a pip python package called kernelml. The motivation for making this algorithm was to give analysts and data scientists a generalized machine learning algorithm for complex loss functions and non-linear coefficients. The optimizer uses a combination of simple machine learning and probabilistic simulations to search for optimal parameters using a loss function, input and output matrices, and (optionally) a random sampler. I'm currently working on more features and hope to eventually make the project open source. Let's take the problem of clustering longitude and latitude coordinates.

I created a custom'particle optimizer' and published a pip python package called kernelml. The motivation for making this algorithm was to give analysts and data scientists a generalized machine learning algorithm for complex loss functions and non-linear coefficients. The optimizer uses a combination of simple machine learning and probabilistic simulations to search for optimal parameters using a loss function, input and output matrices, and (optionally) a random sampler. I'm currently working on more features and hope to eventually make the project open source. Lets take the problem of clustering longitude and latitude coordinates.