Most convex and nonconvex clustering algorithms come with one crucial parameter: the $k$ in $k$-means. To this day, there is not one generally accepted way to accurately determine this parameter. Popular methods are simple yet theoretically unfounded, such as searching for an elbow in the curve of a given cost measure. In contrast, statistically founded methods often make strict assumptions over the data distribution or come with their own optimization scheme for the clustering objective. This limits either the set of applicable datasets or clustering algorithms. In this paper, we strive to determine the number of clusters by answering a simple question: given two clusters, is it likely that they jointly stem from a single distribution? To this end, we propose a bound on the probability that two clusters originate from the distribution of the unified cluster, specified only by the sample mean and variance. Our method is applicable as a simple wrapper to the result of any clustering method minimizing the objective of $k$-means, which includes Gaussian mixtures and Spectral Clustering. We focus in our experimental evaluation on an application for nonconvex clustering and demonstrate the suitability of our theoretical results. Our \textsc{SpecialK} clustering algorithm automatically determines the appropriate value for $k$, without requiring any data transformation or projection, and without assumptions on the data distribution. Additionally, it is capable to decide that the data consists of only a single cluster, which many existing algorithms cannot.

This paper addresses the data-driven identification of latent dynamical representations of partially-observed systems, i.e., dynamical systems for which some components are never observed, with an emphasis on forecasting applications, including long-term asymptotic patterns. Whereas state-of-the-art data-driven approaches rely on delay embeddings and linear decompositions of the underlying operators, we introduce a framework based on the data-driven identification of an augmented state-space model using a neural-network-based representation. For a given training dataset, it amounts to jointly learn an ODE (Ordinary Differential Equation) representation in the latent space and reconstructing latent states. Through numerical experiments, we demonstrate the relevance of the proposed framework w.r.t. state-of-the-art approaches in terms of short-term forecasting performance and long-term behaviour. We further discuss how the proposed framework relates to Koopman operator theory and Takens' embedding theorem.

In recent years, there have been significant efforts on mitigating unethical demographic biases in machine learning methods. However, very little is done for kernel methods. In this paper, we propose a new fair kernel regression method via fair feature embedding (FKR-F$^2$E) in kernel space. Motivated by prior works on feature selection in kernel space and feature processing for fair machine learning, we propose to learn fair feature embedding functions that minimize demographic discrepancy of feature distributions in kernel space. Compared to the state-of-the-art fair kernel regression method and several baseline methods, we show FKR-F$^2$E achieves significantly lower prediction disparity across three real-world data sets.

Experience Management studies AI systems that automatically adapt interactive experiences such as games to tailor to specific players and to fulfill design goals. Although it has been explored for several decades, existing work in experience management has mostly focused on single-player experiences. This paper is a first attempt at identifying the main challenges to expand EM to multi-player/multi-user games or experiences. We also make connections to related areas where solutions for similar problems have been proposed (especially group recommender systems) and discusses the potential impact and applications of multi-player EM.

We present ARU, an Adaptive Recurrent Unit for streaming adaptation of deep globally trained time-series forecasting models. The ARU combines the advantages of learning complex data transformations across multiple time series from deep global models, with per-series localization offered by closed-form linear models. Unlike existing methods of adaptation that are either memory-intensive or non-responsive after training, ARUs require only fixed sized state and adapt to streaming data via an easy RNN-like update operation. The core principle driving ARU is simple --- maintain sufficient statistics of conditional Gaussian distributions and use them to compute local parameters in closed form. Our contribution is in embedding such local linear models in globally trained deep models while allowing end-to-end training on the one hand, and easy RNN-like updates on the other. Across several datasets we show that ARU is more effective than recently proposed local adaptation methods that tax the global network to compute local parameters.

We design a new algorithm for the Euclidean $k$-means problem that operates in the local model of differential privacy. Unlike in the non-private literature, differentially private algorithms for the $k$-means incur both additive and multiplicative errors. Our algorithm significantly reduces the additive error while keeping the multiplicative error the same as in previous state-of-the-art results. Specifically, on a database of size $n$, our algorithm guarantees $O(1)$ multiplicative error and $\approx n^{1/2+a}$ additive error for an arbitrarily small constant $a$, whereas all previous algorithms in the local model on had additive error $\approx n^{2/3+a}$. We give a simple lower bound showing that additive error of $\approx\sqrt{n}$ is necessary for $k$-means algorithms in the local model (at least for algorithms with a constant number of interaction rounds, which is the setting we consider in this paper).

AI technologies have the potential to dramatically impact the lives of people with disabilities (PWD). Indeed, improving the lives of PWD is a motivator for many state-of-the-art AI systems, such as automated speech recognition tools that can caption videos for people who are deaf and hard of hearing, or language prediction algorithms that can augment communication for people with speech or cognitive disabilities. However, widely deployed AI systems may not work properly for PWD, or worse, may actively discriminate against them. These considerations regarding fairness in AI for PWD have thus far received little attention. In this position paper, we identify potential areas of concern regarding how several AI technology categories may impact particular disability constituencies if care is not taken in their design, development, and testing. We intend for this risk assessment of how various classes of AI might interact with various classes of disability to provide a roadmap for future research that is needed to gather data, test these hypotheses, and build more inclusive algorithms.

With the recent advances in complex networks theory, graph-based techniques for image segmentation has attracted great attention recently. In order to segment the image into meaningful connected components, this paper proposes an image segmentation general framework using complex networks based community detection algorithms. If we consider regions as communities, using community detection algorithms directly can lead to an over-segmented image. To address this problem, we start by splitting the image into small regions using an initial segmentation. The obtained regions are used for building the complex network. To produce meaningful connected components and detect homogeneous communities, some combinations of color and texture based features are employed in order to quantify the regions similarities. To sum up, the network of regions is constructed adaptively to avoid many small regions in the image, and then, community detection algorithms are applied on the resulting adaptive similarity matrix to obtain the final segmented image. Experiments are conducted on Berkeley Segmentation Dataset and four of the most influential community detection algorithms are tested. Experimental results have shown that the proposed general framework increases the segmentation performances compared to some existing methods.

We find that by and large GANs fail to faithfully datasets. To our knowledge, the only instance of synthetic recreate point datasets which contain discontinous image datasets used for GAN evaluation have been to learn support or sharp bends with noise. Additionally, manifolds of convex polygons (specifically triangles) (Lucic on image datasets, we find that GANs do et al., 2018). Although, we also use polygons as a testbed not seem to learn to count the number of objects for our experiments, we focus on learning a manifold with of the same kind in an image. We also highlight multiple polygons where their number is fixed.

We present a framework for compactly summarizing many recent results in efficient and/or biologically plausible online training of recurrent neural networks (RNN). The framework organizes algorithms according to several criteria: (a) past vs. future facing, (b) tensor structure, (c) stochastic vs. deterministic, and (d) closed form vs. numerical. These axes reveal latent conceptual connections among several recent advances in online learning. Furthermore, we provide novel mathematical intuitions for their degree of success. Testing various algorithms on two synthetic tasks shows that performances cluster according to our criteria. Although a similar clustering is also observed for gradient alignment, alignment with exact methods does not alone explain ultimate performance, especially for stochastic algorithms. This suggests the need for better comparison metrics.