Can I become a data scientist with little or no math background? What essential math skills are important in data science? There are so many good packages that can be used for building predictive models or for producing data visualizations. Thanks to these packages, anyone can build a model or produce a data visualization. However, very solid background knowledge in mathematics is essential for fine-tuning your models to produce reliable models with optimal performance.

Yim, what have you been working on for the past 2 years? It's this paper that just got accepted at the ACM International Computing Education Research (ICER) conference! Here's a pre-print of the paper: Learning Machine Learning with Personal Data Helps Stakeholders Ground Advocacy Arguments in Model Mechanics (Yim Register & Amy J. Ko, 2020) Gotta love academic titles am I right? But don't worry, I've saved you the trouble of reading the paper by summarizing it in this blog post. Because A) honestly, it is long and fancy and a bit jargony and B) because how else would you get to read all my jokes?

Are you getting different results for your machine learning algorithm? Perhaps your results differ from a tutorial and you want to understand why. Perhaps your model is making different predictions each time it is trained, even when it is trained on the same data set each time. This is to be expected and might even be a feature of the algorithm, not a bug. In this tutorial, you will discover why you can expect different results when using machine learning algorithms. Why Do I Get Different Results Each Time in Machine Learning?

A method to predict time-series using multiple deep learners and a Bayesian network is proposed. In this study, the input explanatory variables are Bayesian network nodes that are associated with learners. Training data are divided using K-means clustering, and multiple deep learners are trained depending on the cluster. A Bayesian network is used to determine which deep learner is in charge of predicting a time-series. We determine a threshold value and select learners with a posterior probability equal to or greater than the threshold value, which could facilitate more robust prediction. The proposed method is applied to financial time-series data, and the predicted results for the Nikkei 225 index are demonstrated.

Grassmann manifold based sparse spectral clustering is a classification technique that  consists in learning a latent representation of data, formed by a subspace basis, which  is sparse. In order to learn a latent representation, spectral clustering is formulated in  terms of a loss minimization problem over a smooth manifold known as Grassmannian.  Such minimization problem cannot be tackled by one of traditional gradient-based learning  algorithms, which are only suitable to perform optimization in absence of constraints among  parameters. It is, therefore, necessary to develop specific optimization/learning algorithms  that are able to look for a local minimum of a loss function under smooth constraints in  an efficient way. Such need calls for manifold optimization methods. In this paper, we  extend classical gradient-based learning algorithms on   at parameter spaces (from classical  gradient descent to adaptive momentum) to curved spaces (smooth manifolds) by means  of tools from manifold calculus. We compare clustering performances of these methods  and known methods from the scientific literature. The obtained results confirm that the  proposed learning algorithms prove lighter in computational complexity than existing ones  without detriment in clustering efficacy.

The perception of color is an important cognitive feature of the human brain. The variety of colors that impinge upon the human eye can trigger changes in brain activity which can be captured using electroencephalography (EEG). In this work, we have designed a multiclass classification model to detect the primary colors from the features of raw EEG signals. In contrast to previous research, our method employs spectral power features, statistical features as well as correlation features from the signal band power obtained from continuous Morlet wavelet transform instead of raw EEG, for the classification task. We have applied dimensionality reduction techniques such as Forward Feature Selection and Stacked Autoencoders to reduce the dimension of data eventually increasing the model's efficiency. Our proposed methodology using Forward Selection and Random Forest Classifier gave the best overall accuracy of 80.6\% for intra-subject classification. Our approach shows promise in developing techniques for cognitive tasks using color cues such as controlling Internet of Thing (IoT) devices by looking at primary colors for individuals with restricted motor abilities.

Brain connectivity networks, which characterize the functional or structural interaction of brain regions, has been widely used for brain disease classification. Kernel-based method, such as graph kernel (i.e., kernel defined on graphs), has been proposed for measuring the similarity of brain networks, and yields the promising classification performance. However, most of graph kernels are built on unweighted graph (i.e., network) with edge present or not, and neglecting the valuable weight information of edges in brain connectivity network, with edge weights conveying the strengths of temporal correlation or fiber connection between brain regions. Accordingly, in this paper, we present an ordinal pattern kernel for brain connectivity network classification. Different with existing graph kernels that measures the topological similarity of unweighted graphs, the proposed ordinal pattern kernels calculate the similarity of weighted networks by comparing ordinal patterns from weighted networks. To evaluate the effectiveness of the proposed ordinal kernel, we further develop a depth-first-based ordinal pattern kernel, and perform extensive experiments in a real dataset of brain disease from ADNI database. The results demonstrate that our proposed ordinal pattern kernel can achieve better classification performance compared with state-of-the-art graph kernels.

Node embeddings have been attracting increasing attention during the past years. In this context, we propose a new ensemble node embedding approach, called TenSemble2Vec, by first generating multiple embeddings using the existing techniques and taking them as multiview data input of the state-of-art tensor decomposition model namely PARAFAC2 to learn the shared lower-dimensional representations of the nodes. Contrary to other embedding methods, our TenSemble2Vec takes advantage of the complementary information from different methods or the same method with different hyper-parameters, which bypasses the challenge of choosing models. Extensive tests using real-world data validates the efficiency of the proposed method.

We design layerwise objectives as functionals whose analytic minimizers sufficiently express the exact ground-truth network in terms of its parameters and nonlinearities. Following this objective landscape, learning a preReLU-TLRN from finite samples can be formulated as convex programming with nonparametric function estimation: For each layer, we first formulate the corresponding empirical risk minimization (ERM) as convex quadratic programming (QP), then we show the solution space of the QP can be equivalently determined by a set of linear inequalities, which can then be efficiently solved by linear programming (LP). Experiments show the robustness and sample efficiency of our methods.

Gradient descent is a popular algorithm in optimization, and its performance in convex settings is mostly well understood. In non-convex settings, it has been shown that gradient descent is able to escape saddle points asymptotically and converge to local minimizers [Lee et. al. 2016]. Recent studies also show a perturbed version of gradient descent is enough to escape saddle points efficiently [Jin et. al. 2015, Ge et. al. 2017]. In this paper we show a negative result: gradient descent may take exponential time to escape saddle points, with non-pathological two dimensional functions. While our focus is theoretical, we also conduct experiments verifying our theoretical result. Through our analysis we demonstrate that stochasticity is essential to escape saddle points efficiently.