We show how to solve a number of problems in numerical linear algebra, such as least squares regression, $\ell_p$-regression for any $p \geq 1$, low rank approximation, and kernel regression, in time $T(A) \poly(\log(nd))$, where for a given input matrix $A \in \mathbb{R}^{n \times d}$, $T(A)$ is the time needed to compute $A\cdot y$ for an arbitrary vector $y \in \mathbb{R}^d$. Since $T(A) \leq O(\nnz(A))$, where $\nnz(A)$ denotes the number of non-zero entries of $A$, the time is no worse, up to polylogarithmic factors, as all of the recent advances for such problems that run in input-sparsity time. However, for many applications, $T(A)$ can be much smaller than $\nnz(A)$, yielding significantly sublinear time algorithms. For example, in the overconstrained $(1+\epsilon)$-approximate polynomial interpolation problem, $A$ is a Vandermonde matrix and $T(A) = O(n \log n)$; in this case our running time is $n \cdot \poly(\log n) + \poly(d/\epsilon)$ and we recover the results of \cite{avron2013sketching} as a special case. For overconstrained autoregression, which is a common problem arising in dynamical systems, $T(A) = O(n \log n)$, and we immediately obtain $n \cdot \poly(\log n) + \poly(d/\epsilon)$ time. For kernel autoregression, we significantly improve the running time of prior algorithms for general kernels. For the important case of autoregression with the polynomial kernel and arbitrary target vector $b\in\mathbb{R}^n$, we obtain even faster algorithms. Our algorithms show that, perhaps surprisingly, most of these optimization problems do not require much more time than that of a polylogarithmic number of matrix-vector multiplications.

Graph Convolutional Networks (GCNs) have gained significant developments in representation learning on graphs. However, current GCNs suffer from two common challenges: 1) GCNs are only effective with shallow structures; stacking multiple GCN layers will lead to over-smoothing. 2) GCNs do not scale well with large, dense graphs due to the recursive neighborhood expansion. We generalize the propagation strategies of current GCNs as a \emph{"Sink$\to$Source"} mode, which seems to be an underlying cause of the two challenges. To address these issues intrinsically, in this paper, we study the information propagation mechanism in a \emph{"Source$\to$Sink"} mode. We introduce a new concept "information flow path" that explicitly defines where information originates and how it diffuses. Then a novel framework, namely Flow Graph Network (FlowGN), is proposed to learn node representations. FlowGN is computationally efficient and flexible in propagation strategies. Moreover, FlowGN decouples the layer structure from the information propagation process, removing the interior constraint of applying deep structures in traditional GCNs. Further experiments on public datasets demonstrate the superiority of FlowGN against state-of-the-art GCNs.

Machine Learning (ML) has been applied to enable many life-assisting appli-cations, such as abnormality detection and emdergency request for the soli-tary elderly. However, in most cases machine learning algorithms depend on the layout of the target Internet of Things (IoT) sensor network. Hence, to deploy an application across Heterogeneous Sensor Networks (HSNs), i.e. sensor networks with different sensors type or layouts, it is required to repeat the process of data collection and ML algorithm training. In this paper, we introduce a novel framework leveraging deep learning for graphs to enable using the same activity recognition system across HSNs deployed in differ-ent smart homes. Using our framework, we were able to transfer activity classifiers trained with activity labels on a source HSN to a target HSN, reaching about 75% of the baseline accuracy on the target HSN without us-ing target activity labels. Moreover, our model can quickly adapt to unseen sensor layouts, which makes it highly suitable for the gradual deployment of real-world ML-based applications. In addition, we show that our framework is resilient to suboptimal graph representations of HSNs.

Model misspecification is a long-standing enigma of the Bayesian inference framework as posteriors tend to get overly concentrated on ill-informed parameter values towards the large sample limit. Tempering of the likelihood has been established as a safer way to do updates from prior to posterior in the presence of model misspecification. At one extreme tempering can ignore the data altogether and at the other extreme it provides the standard Bayes' update when no misspecification is assumed to be present. However, it is an open issue how to best recognize misspecification and choose a suitable level of tempering without access to the true generating model. Here we show how probabilistic classifiers can be employed to resolve this issue. By training a probabilistic classifier to discriminate between simulated and observed data provides an estimate of the ratio between the model likelihood and the likelihood of the data under the unobserved true generative process, within the discriminatory abilities of the classifier. The expectation of the logarithm of a ratio with respect to the data generating process gives an estimation of the negative Kullback-Leibler divergence between the statistical generative model and the true generative distribution. Using a set of canonical examples we show that this divergence provides a useful misspecification diagnostic, a model comparison tool, and a method to inform a generalised Bayesian update in the presence of misspecification for likelihood-based models.

While Bayesian neural networks have many appealing characteristics, current priors do not easily allow users to specify basic properties such as expected lengthscale or amplitude variance. In this work, we introduce Poisson Process Radial Basis Function Networks, a novel prior that is able to encode amplitude stationarity and input-dependent lengthscale. We prove that our novel formulation allows for a decoupled specification of these properties, and that the estimated regression function is consistent as the number of observations tends to infinity. We demonstrate its behavior on synthetic and real examples.

The ability to inferring latent psychological traits from human behavior is key to developing personalized human-interacting machine learning systems. Approaches to infer such traits range from surveys to manually-constructed experiments and games. However, these traditional games are limited because they are typically designed based on heuristics. In this paper, we formulate the task of designing \emph{behavior diagnostic games} that elicit distinguishable behavior as a mutual information maximization problem, which can be solved by optimizing a variational lower bound. Our framework is instantiated by using prospect theory to model varying player traits, and Markov Decision Processes to parameterize the games. We validate our approach empirically, showing that our designed games can successfully distinguish among players with different traits, outperforming manually-designed ones by a large margin.

Before choosing a machine learning algorithm, it's important to know their characteristics to generate desired outputs and build smart systems. Data science is growing super fast. As the demand for AI-enabled solutions is increasing, delivering smarter systems for industries has become essential. And the correctness and efficiency through machine learning operations must be fulfilled to ensure the developed solutions complete all demands. Hence, applying machine learning algorithms on the given dataset to produce righteous results and train the intelligent system is one of the most essential steps from the entire process.

Robotics Process Automation (RPA) is a technology that helps you in automating your business process. It is a technology which mimic human actions in interacting with digital system. To understand what's RPA in a more intuitive way: What can RPA do for you? UiPath is one of the top leaders which develops Robotics Process Automation platforms. By deploying RPA into your business process, it helps your business in reducing operation cost, eliminate human error and saving time.

With the incorporation of new data gathering methods in clinical research, it becomes fundamental for survival analysis techniques to deal with high-dimensional or/and non-standard covariates. In this paper we introduce a general non-parametric independence test between right-censored survival times and covariates taking values on a general (not necessarily Euclidean) space X. We show that our test statistic has a dual interpretation, first in terms of the supremum of a potentially infinite collection of weight-indexed log-rank tests, with weight functions belonging to a reproducing kernel Hilbert space (RKHS) of functions; and second, as the norm of the difference of embeddings of certain finite measures into the RKHS, similar to the Hilbert-Schmidt Independence Criterion (HSIC) test-statistic. We study the asymptotic properties of the test, finding sufficient conditions to ensure that our test is omnibus. The test statistic can be computed straightforwardly, and the rejection threshold is obtained via an asymptotically consistent Wild-Bootstrap procedure.