Wefocusonsixmethods:(i)discriminative K-means (DisKmeans) in Ye et al. (2008); (ii) a discriminative clustering formulation described inBach andHarchaoui (2008); Flammarion etal.(2017); We compare two classesF of feature mappings: linear functions and fully-connected neural networks with one hidden layer that has 100 nodes. An epoch refers ton/B = 12 consecutive iterations. The learning curves in Figure 1 shows the advantage of neural network and demonstrates the flexibility of CURE with nonlinear function classes. One of the main obstacles is the complicated piecewise definition off, which prevent us from obtaining closed form formulae.

Clustering is a fundamental problem in data science, especially in the early stages of knowledge discovery.

Generative modeling of multivariate time series has remained challenging partly due to the complex, non-deterministic dynamics across long-distance time steps. In this paper, we propose deep probabilistic methods that combine state-space models (SSMs) with transformer architectures. In contrast to previously proposed SSMs, our approaches use attention mechanism to model non-Markovian dynamics in the latent space and avoid recurrent neural networks entirely. We also extend our models to include several layers of stochastic variables organized in a hierarchy for further expressiveness. Compared to transformer models, ours are probabilistic, non-autoregressive, and capable of generating diverse long-term forecasts with accounted uncertainty. Extensive experiments show that our models consistently outperform competitive baselines on various tasks and datasets, including time series forecasting and human motion prediction.

In image retrieval, standard evaluation metrics rely on score ranking, e.g.