The study of biological processes can greatly benefit from tools that automatically predict gene functions or directly cluster genes based on shared functionality. Existing data mining methods predict protein functionality by exploiting data obtained from high-throughput experiments or meta-scale information from public databases. Most existing prediction tools are targeted at predicting protein functions that are described in the gene ontology (GO). However, in many cases biologists wish to discover functionally related genes for which GO terms are inadequate. In this paper, we introduce a rich set of features and use them in conjunction with semisupervised learning approaches in order to expand an initial set of seed genes to a larger cluster of functionally related genes. Among all the semi-supervised methods that were evaluated, the framework of learning with positive and unlabeled examples (LPU) is shown to be especially appropriate for mining functionally related genes. When evaluated on experimentally validated benchmark data, the LPU approaches1 significantly outperform a standard supervised learning algorithm as well as an established state-of-the-art method. Given an initial set of seed genes, our best performing approach could be used to mine functionally related genes in a wide range of organisms.

In this section we will learn - What does Machine Learning mean. What are the meanings or different terms associated with machine learning? You will see some examples so that you understand what machine learning actually is. It also contains steps involved in building a machine learning model, not just linear models, any machine learning model.

In this paper, we introduce convolutional proximal neural networks (cPNNs), which are by construction averaged operators. For filters of full length, we propose a stochastic gradient descent algorithm on a submanifold of the Stiefel manifold to train cPNNs. In case of filters with limited length, we design algorithms for minimizing functionals that approximate the orthogonality constraints imposed on the operators by penalizing the least squares distance to the identity operator. Then, we investigate how scaled cPNNs with a prescribed Lipschitz constant can be used for denoising signals and images, where the achieved quality depends on the Lipschitz constant. Finally, we apply cPNN based denoisers within a Plug-and-Play (PnP) framework and provide convergence results for the corresponding PnP forward-backward splitting algorithm based on an oracle construction.

Esports, despite its expanding interest, lacks fundamental sports analytics resources such as accessible data or proven and reproducible analytical frameworks. Even Counter-Strike: Global Offensive (CSGO), the second most popular esport, suffers from these problems. Thus, quantitative evaluation of CSGO players, a task important to teams, media, bettors and fans, is difficult. To address this, we introduce (1) a data model for CSGO with an open-source implementation; (2) a graph distance measure for defining distances in CSGO; and (3) a context-aware framework to value players' actions based on changes in their team's chances of winning. Using over 70 million in-game CSGO events, we demonstrate our framework's consistency and independence compared to existing valuation frameworks. We also provide use cases demonstrating high-impact play identification and uncertainty estimation.

Learning to quantify (a.k.a.\ quantification) is a task concerned with training unbiased estimators of class prevalence via supervised learning. This task originated with the observation that "Classify and Count" (CC), the trivial method of obtaining class prevalence estimates, is often a biased estimator, and thus delivers suboptimal quantification accuracy; following this observation, several methods for learning to quantify have been proposed that have been shown to outperform CC. In this work we contend that previous works have failed to use properly optimised versions of CC. We thus reassess the real merits of CC (and its variants), and argue that, while still inferior to some cutting-edge methods, they deliver near-state-of-the-art accuracy once (a) hyperparameter optimisation is performed, and (b) this optimisation is performed by using a true quantification loss instead of a standard classification-based loss. Experiments on three publicly available binary sentiment classification datasets support these conclusions.

Digital payment volume has proliferated in recent years with the rapid growth of small businesses and online shops. When processing these digital transactions, recognizing each merchant's real identity (i.e., business type) is vital to ensure the integrity of payment processing systems. Conventionally, this problem is formulated as a time series classification problem solely using the merchant transaction history. However, with the large scale of the data, and changing behaviors of merchants and consumers over time, it is extremely challenging to achieve satisfying performance from off-the-shelf classification methods. In this work, we approach this problem from a multi-modal learning perspective, where we use not only the merchant time series data but also the information of merchant-merchant relationship (i.e., affinity) to verify the self-reported business type (i.e., merchant category) of a given merchant. Specifically, we design two individual encoders, where one is responsible for encoding temporal information and the other is responsible for affinity information, and a mechanism to fuse the outputs of the two encoders to accomplish the identification task. Our experiments on real-world credit card transaction data between 71,668 merchants and 433,772,755 customers have demonstrated the effectiveness and efficiency of the proposed model.

Sentiment quantification is the task of estimating the relative frequency (or "prevalence") of sentiment-related classes (such as Positive, Neutral, Negative) in a sample of unlabelled texts; this is especially important when these texts are tweets, since most sentiment classification endeavours carried out on Twitter data actually have quantification (and not the classification of individual tweets) as their ultimate goal. It is well-known that solving quantification via "classify and count" (i.e., by classifying all unlabelled items via a standard classifier and counting the items that have been assigned to a given class) is suboptimal in terms of accuracy, and that more accurate quantification methods exist. In 2016, Gao and Sebastiani carried out a systematic comparison of quantification methods on the task of tweet sentiment quantification. In hindsight, we observe that the experimental protocol followed in that work is flawed, and that its results are thus unreliable. We now re-evaluate those quantification methods on the very same datasets, this time following a now consolidated and much more robust experimental protocol, that involves 5775 as many experiments as run in the original study. Our experimentation yields results dramatically different from those obtained by Gao and Sebastiani, and thus provide a different, much more solid understanding of the relative strengths and weaknesses of different sentiment quantification methods.

Understanding the algorithmic regularization effect of stochastic gradient descent (SGD) is one of the key challenges in modern machine learning and deep learning theory. Most of the existing works, however, focus on very small or even infinitesimal learning rate regime, and fail to cover practical scenarios where the learning rate is moderate and annealing. In this paper, we make an initial attempt to characterize the particular regularization effect of SGD in the moderate learning rate regime by studying its behavior for optimizing an overparameterized linear regression problem. In this case, SGD and GD are known to converge to the unique minimum-norm solution; however, with the moderate and annealing learning rate, we show that they exhibit different directional bias: SGD converges along the large eigenvalue directions of the data matrix, while GD goes after the small eigenvalue directions. Furthermore, we show that such directional bias does matter when early stopping is adopted, where the SGD output is nearly optimal but the GD output is suboptimal. Finally, our theory explains several folk arts in practice used for SGD hyperparameter tuning, such as (1) linearly scaling the initial learning rate with batch size; and (2) overrunning SGD with high learning rate even when the loss stops decreasing.

In this paper, we consider the problem of empirical risk minimization (ERM) of smooth, strongly convex loss functions using iterative gradient-based methods. A major goal of this literature has been to compare different algorithms, such as gradient descent (GD) or stochastic gradient descent (SGD), by analyzing their rates of convergence to $\epsilon$-approximate solutions. For example, the oracle complexity of GD is $O(n\log(\epsilon^{-1}))$, where $n$ is the number of training samples. When $n$ is large, this can be expensive in practice, and SGD is preferred due to its oracle complexity of $O(\epsilon^{-1})$. Such standard analyses only utilize the smoothness of the loss function in the parameter being optimized. In contrast, we demonstrate that when the loss function is smooth in the data, we can learn the oracle at every iteration and beat the oracle complexities of both GD and SGD in important regimes. Specifically, at every iteration, our proposed algorithm performs local polynomial regression to learn the gradient of the loss function, and then estimates the true gradient of the ERM objective function. We establish that the oracle complexity of our algorithm scales like $\tilde{O}((p \epsilon^{-1})^{d/(2\eta)})$ (neglecting sub-dominant factors), where $d$ and $p$ are the data and parameter space dimensions, respectively, and the gradient of the loss function belongs to a $\eta$-H\"{o}lder class with respect to the data. Our proof extends the analysis of local polynomial regression in non-parametric statistics to provide interpolation guarantees in multivariate settings, and also exploits tools from the inexact GD literature. Unlike GD and SGD, the complexity of our method depends on $d$ and $p$. However, when $d$ is small and the loss function exhibits modest smoothness in the data, our algorithm beats GD and SGD in oracle complexity for a very broad range of $p$ and $\epsilon$.

For a function $\mathsf{K} : \mathbb{R}^{d} \times \mathbb{R}^{d} \to \mathbb{R}_{\geq 0}$, and a set $P = \{ x_1, \ldots, x_n\} \subset \mathbb{R}^d$ of $n$ points, the $\mathsf{K}$ graph $G_P$ of $P$ is the complete graph on $n$ nodes where the weight between nodes $i$ and $j$ is given by $\mathsf{K}(x_i, x_j)$. In this paper, we initiate the study of when efficient spectral graph theory is possible on these graphs. We investigate whether or not it is possible to solve the following problems in $n^{1+o(1)}$ time for a $\mathsf{K}$-graph $G_P$ when $d < n^{o(1)}$: $\bullet$ Multiply a given vector by the adjacency matrix or Laplacian matrix of $G_P$ $\bullet$ Find a spectral sparsifier of $G_P$ $\bullet$ Solve a Laplacian system in $G_P$'s Laplacian matrix For each of these problems, we consider all functions of the form $\mathsf{K}(u,v) = f(\|u-v\|_2^2)$ for a function $f:\mathbb{R} \rightarrow \mathbb{R}$. We provide algorithms and comparable hardness results for many such $\mathsf{K}$, including the Gaussian kernel, Neural tangent kernels, and more. For example, in dimension $d = \Omega(\log n)$, we show that there is a parameter associated with the function $f$ for which low parameter values imply $n^{1+o(1)}$ time algorithms for all three of these problems and high parameter values imply the nonexistence of subquadratic time algorithms assuming Strong Exponential Time Hypothesis ($\mathsf{SETH}$), given natural assumptions on $f$. As part of our results, we also show that the exponential dependence on the dimension $d$ in the celebrated fast multipole method of Greengard and Rokhlin cannot be improved, assuming $\mathsf{SETH}$, for a broad class of functions $f$. To the best of our knowledge, this is the first formal limitation proven about fast multipole methods.