Multi-agent interacting systems are prevalent in the world, from purely physical systems to complicated social dynamic systems. In many applications, effective understanding of the situation and accurate trajectory prediction of interactive agents play a significant role in downstream tasks, such as decision making and planning.

ListNet for instance considers the predicted scores as parameters for the Plackett-Luce distribution [39, 40] and learns these scores via maximum likelihood estimation. Used in a PiRank surrogate loss of Section 3.1, the relaxation presented in Section 3.2 recovers the This finishes the proof by induction. Taking j = d, we obtain from Eq. 22 and the nature of permutation matrices that lim C14, we use "Set 1" which is the larger of the two provided For both datasets, we use the standard train/validation/test splits. The experiments were run on a server with 4 8-core Intel Xeon E5-2620v4 CPUs, 128 GB of RAM and 4 NVIDIA Telsa K80 GPUs. TensorFlow Ranking is licensed under the Apache License 2.0 MSLR-WEB30K is licensed under the Microsoft Research License Agreement (MSR-LA).

Two strategies of evolve-at-changes and history-model-archive are designed to further improve efficiency and stability. Experiments with simulations and neural signals demonstrate that EvoEnsemble can track the changes in functions effectively thus improving the accuracy and robustness of neural decoding. The improvement is most significant in neural signals with functional changes.

We introduce a new theoretical framework to analyze deep learning optimization with connection to its generalization error. Existing frameworks such as mean field theory and neural tangent kernel theory for neural network optimization analysis typically require taking limit of infinite width of the network to show its global convergence. This potentially makes it difficult to directly deal with finite width network; especially in the neural tangent kernel regime, we cannot reveal favorable properties of neural networks beyond kernel methods. To realize more natural analysis, we consider a completely different approach in which we formulate the parameter training as a transportation map estimation and show its global convergence via the theory of the infinite dimensional Langevin dynamics . This enables us to analyze narrow and wide networks in a unifying manner. Moreover, we give generalization gap and excess risk bounds for the solution obtained by the dynamics. The excess risk bound achieves the so-called fast learning rate. In particular, we show an exponential convergence for a classification problem and a minimax optimal rate for a regression problem.

Figure 1: A simple subsplit Bayesian network for a leaf set that contains 4 species A, B, C and D. This figure is adapted from Zhang and Matsen IV (2019). SBN (the one with a full and complete binary tree structure as shown in Figure 1) is good enough. The SBN framework also generalizes to unrooted trees, which are the most common type of phylogenetic trees. (Zhang and Matsen IV, 2018). Sampling from SBNs is also straightforward via ancestral sampling.

We show that VBPI-NF significantly improves upon the vanilla VBPI on a benchmark of challenging real data Bayesian phylogenetic inference problems.