Networks have become indispensable and ubiquitous structures in many fields to model the interactions among different entities, such as friendship in social networks or protein interactions in biological graphs. A major challenge is to understand the structure and dynamics of these systems. Although networks evolve through time, most existing graph representation learning methods target only static networks. Whereas approaches have been developed for the modeling of dynamic networks, there is a lack of efficient continuous time dynamic graph representation learning methods that can provide accurate network characterization and visualization in low dimensions while explicitly accounting for prominent network characteristics such as homophily and transitivity. In this paper, we propose the Piecewise-Velocity Model (PiVeM) for the representation of continuous-time dynamic networks. It learns dynamic embeddings in which the temporal evolution of nodes is approximated by piecewise linear interpolations based on a latent distance model with piecewise constant node-specific velocities. The model allows for analytically tractable expressions of the associated Poisson process likelihood with scalable inference invariant to the number of events. We further impose a scalable Kronecker structured Gaussian Process prior to the dynamics accounting for community structure, temporal smoothness, and disentangled (uncorrelated) latent embedding dimensions optimally learned to characterize the network dynamics. We show that PiVeM can successfully represent network structure and dynamics in ultra-low two-dimensional spaces. It outperforms relevant state-of-art methods in downstream tasks such as link prediction. In summary, PiVeM enables easily interpretable dynamic network visualizations and characterizations that can further improve our understanding of the intrinsic dynamics of time-evolving networks.

A major challenge when using k-means clustering often is how to choose the parameter k, the number of clusters. In this letter, we want to point out that it is very easy to draw poor conclusions from a common heuristic, the "elbow method". Better alternatives have been known in literature for a long time, and we want to draw attention to some of these easy to use options, that often perform better. This letter is a call to stop using the elbow method altogether, because it severely lacks theoretic support, and we want to encourage educators to discuss the problems of the method -- if introducing it in class at all -- and teach alternatives instead, while researchers and reviewers should reject conclusions drawn from the elbow method.

In this work, we propose ModelPred, a framework that helps to understand the impact of changes in training data on a trained model. This is critical for building trust in various stages of a machine learning pipeline: from cleaning poor-quality samples and tracking important ones to be collected during data preparation, to calibrating uncertainty of model prediction, to interpreting why certain behaviors of a model emerge during deployment. Specifically, ModelPred learns a parameterized function that takes a dataset $S$ as the input and predicts the model obtained by training on $S$. Our work differs from the recent work of Datamodels [1] as we aim for predicting the trained model parameters directly instead of the trained model behaviors. We demonstrate that a neural network-based set function class is capable of learning the complex relationships between the training data and model parameters. We introduce novel global and local regularization techniques to prevent overfitting and we rigorously characterize the expressive power of neural networks (NN) in approximating the end-to-end training process. Through extensive empirical investigations, we show that ModelPred enables a variety of applications that boost the interpretability and accountability of machine learning (ML), such as data valuation, data selection, memorization quantification, and model calibration.

Over the years, sequential Monte Carlo (SMC) and, equivalently, particle filter (PF) theory has gained substantial attention from researchers. However, the performance of the resampling methodology, also known as offspring selection, has not advanced recently. We propose two deterministic offspring selection methods, which strive to minimize the Kullback-Leibler (KL) divergence and the total variation (TV) distance, respectively, between the particle distribution prior and subsequent to the offspring selection. By reducing the statistical distance between the selected offspring and the joint distribution, we obtain a heuristic search procedure that performs superior to a maximum likelihood search in precisely those contexts where the latter performs better than an SMC. For SMC and particle Markov chain Monte Carlo (pMCMC), our proposed offspring selection methods always outperform or compare favorably with the two state-of-the-art resampling schemes on two models commonly used as benchmarks from the literature.

There has been an immense progress in the field of machine learning in the last years. In particular, deep learning has led to the development of very complex models which yield highly accurate results but lack explainability and interpretability. To overcome this defect, the field of Explainable Artificial Intelligence (XAI for short, see for example [1-3]) has recently significantly increased momentum.

Automatically generated static code warnings suffer from a large number of false alarms. Hence, developers only take action on a small percent of those warnings. To better predict which static code warnings should not be ignored, we suggest that analysts need to look deeper into their algorithms to find choices that better improve the particulars of their specific problem. Specifically, we show here that effective predictors of such warnings can be created by methods that locally adjust the decision boundary (between actionable warnings and others). These methods yield a new high water-mark for recognizing actionable static code warnings. For eight open-source Java projects (cassandra, jmeter, commons, lucene-solr, maven, ant, tomcat, derby) we achieve perfect test results on 4/8 datasets and, overall, a median AUC (area under the true negatives, true positives curve) of 92%.

A canonical algorithm for log-concave sampling is the Langevin Algorithm, aka the Langevin Diffusion run with some discretization stepsize $\eta > 0$. This discretization leads the Langevin Algorithm to have a stationary distribution $\pi_{\eta}$ which differs from the stationary distribution $\pi$ of the Langevin Diffusion, and it is an important challenge to understand whether the well-known properties of $\pi$ extend to $\pi_{\eta}$. In particular, while concentration properties such as isoperimetry and rapidly decaying tails are classically known for $\pi$, the analogous properties for $\pi_{\eta}$ are open questions with direct algorithmic implications. This note provides a first step in this direction by establishing concentration results for $\pi_{\eta}$ that mirror classical results for $\pi$. Specifically, we show that for any nontrivial stepsize $\eta > 0$, $\pi_{\eta}$ is sub-exponential (respectively, sub-Gaussian) when the potential is convex (respectively, strongly convex). Moreover, the concentration bounds we show are essentially tight. Key to our analysis is the use of a rotation-invariant moment generating function (aka Bessel function) to study the stationary dynamics of the Langevin Algorithm. This technique may be of independent interest because it enables directly analyzing the discrete-time stationary distribution $\pi_{\eta}$ without going through the continuous-time stationary distribution $\pi$ as an intermediary.

The visual world can be parsimoniously characterized in terms of distinct entities with sparse interactions. Discovering this compositional structure in dynamic visual scenes has proven challenging for end-to-end computer vision approaches unless explicit instance-level supervision is provided. Slot-based models leveraging motion cues have recently shown great promise in learning to represent, segment, and track objects without direct supervision, but they still fail to scale to complex real-world multi-object videos. In an effort to bridge this gap, we take inspiration from human development and hypothesize that information about scene geometry in the form of depth signals can facilitate object-centric learning. We introduce SAVi++, an object-centric video model which is trained to predict depth signals from a slot-based video representation. By further leveraging best practices for model scaling, we are able to train SAVi++ to segment complex dynamic scenes recorded with moving cameras, containing both static and moving objects of diverse appearance on naturalistic backgrounds, without the need for segmentation supervision. Finally, we demonstrate that by using sparse depth signals obtained from LiDAR, SAVi++ is able to learn emergent object segmentation and tracking from videos in the real-world Waymo Open dataset.

Warfarin is a widely used anticoagulant, and has a narrow therapeutic range. Dosing of warfarin should be individualized, since slight overdosing or underdosing can have catastrophic or even fatal consequences. Despite much research on warfarin dosing, current dosing protocols do not live up to expectations, especially for patients sensitive to warfarin. We propose a deep reinforcement learning-based dosing model for warfarin. To overcome the issue of relatively small sample sizes in dosing trials, we use a Pharmacokinetic/ Pharmacodynamic (PK/PD) model of warfarin to simulate dose-responses of virtual patients. Applying the proposed algorithm on virtual test patients shows that this model outperforms a set of clinically accepted dosing protocols by a wide margin. We tested the robustness of our dosing protocol on a second PK/PD model and showed that its performance is comparable to the set of baseline protocols.

Among many clustering algorithms, the K-means clustering algorithm is widely used because of its simple algorithm and fast convergence. However, this algorithm suffers from incomplete data, where some samples have missed some of their attributes. To solve this problem, we mainly apply MM principles to restore the symmetry of the data, so that K-means could work well. We give the pseudo-code of the algorithm and use the standard datasets for experimental verification. Clustering is the task of grouping a set of objects in such a way that objects in the same group (called a cluster) are more similar (in some sense or another) to each other than to those in other groups (clusters). It is the main task of exploratory data mining, and a common technique for statistical data analysis used in many fields, including machine learning, pattern recognition, image analysis, information retrieval, and bioinformatics [1]-[3].