Shidi Li

Shidi Li, Christian Walder, Alexander Soen et al.

The sparse transformer can reduce the computational complexity of the self-attention layers to $O(n)$, whilst still being a universal approximator of continuous sequence-to-sequence functions. However, this permutation variant operation is not appropriate for direct application to sets. In this paper, we proposed an $O(n)$ complexity sampled transformer that can process point set elements directly without any additional inductive bias. Our sampled transformer introduces random element sampling, which randomly splits point sets into subsets, followed by applying a shared Hamiltonian self-attention mechanism to each subset. The overall attention mechanism can be viewed as a Hamiltonian cycle in the complete attention graph, and the permutation of point set elements is equivalent to randomly sampling Hamiltonian cycles. This mechanism implements a Monte Carlo simulation of the $O(n^2)$ dense attention connections. We show that it is a universal approximator for continuous set-to-set functions. Experimental results on point-clouds show comparable or better accuracy with significantly reduced computational complexity compared to the dense transformer or alternative sparse attention schemes.

Shidi Li, Christian Walder, Miaomiao Liu

This paper addresses the problem of unsupervised parts-aware point cloud generation with learned parts-based self-similarity. Our SPA-VAE infers a set of latent canonical candidate shapes for any given object, along with a set of rigid body transformations for each such candidate shape to one or more locations within the assembled object. In this way, noisy samples on the surface of, say, each leg of a table, are effectively combined to estimate a single leg prototype. When parts-based self-similarity exists in the raw data, sharing data among parts in this way confers numerous advantages: modeling accuracy, appropriately self-similar generative outputs, precise in-filling of occlusions, and model parsimony. SPA-VAE is trained end-to-end using a variational Bayesian approach which uses the Gumbel-softmax trick for the shared part assignments, along with various novel losses to provide appropriate inductive biases. Quantitative and qualitative analyses on ShapeNet demonstrate the advantage of SPA-VAE.

Shidi Li, Miaomiao Liu, Christian Walder

This paper tackles the problem of parts-aware point cloud generation. Unlike existing works which require the point cloud to be segmented into parts a priori, our parts-aware editing and generation are performed in an unsupervised manner. We achieve this with a simple modification of the Variational Auto-Encoder which yields a joint model of the point cloud itself along with a schematic representation of it as a combination of shape primitives. In particular, we introduce a latent representation of the point cloud which can be decomposed into a disentangled representation for each part of the shape. These parts are in turn disentangled into both a shape primitive and a point cloud representation, along with a standardising transformation to a canonical coordinate system. The dependencies between our standardising transformations preserve the spatial dependencies between the parts in a manner that allows meaningful parts-aware point cloud generation and shape editing. In addition to the flexibility afforded by our disentangled representation, the inductive bias introduced by our joint modeling approach yields state-of-the-art experimental results on the ShapeNet dataset.

Marian-Andrei Rizoiu, Alexander Soen, Shidi Li et al.

Interval-censored data solely records the aggregated counts of events during specific time intervals - such as the number of patients admitted to the hospital or the volume of vehicles passing traffic loop detectors - and not the exact occurrence time of the events. It is currently not understood how to fit the Hawkes point processes to this kind of data. Its typical loss function (the point process log-likelihood) cannot be computed without exact event times. Furthermore, it does not have the independent increments property to use the Poisson likelihood. This work builds a novel point process, a set of tools, and approximations for fitting Hawkes processes within interval-censored data scenarios. First, we define the Mean Behavior Poisson process (MBPP), a novel Poisson process with a direct parameter correspondence to the popular self-exciting Hawkes process. We fit MBPP in the interval-censored setting using an interval-censored Poisson log-likelihood (IC-LL). We use the parameter equivalence to uncover the parameters of the associated Hawkes process. Second, we introduce two novel exogenous functions to distinguish the exogenous from the endogenous events. We propose the multi-impulse exogenous function - for when the exogenous events are observed as event time - and the latent homogeneous Poisson process exogenous function - for when the exogenous events are presented as interval-censored volumes. Third, we provide several approximation methods to estimate the intensity and compensator function of MBPP when no analytical solution exists. Fourth and finally, we connect the interval-censored loss of MBPP to a broader class of Bregman divergence-based functions. Using the connection, we show that the popularity estimation algorithm Hawkes Intensity Process (HIP) is a particular case of the MBPP. We verify our models through empirical testing on synthetic data and real-world data.

Shidi Li

Several model-based and model-free methods have been proposed for the robot trajectory learning task. Both approaches have their benefits and drawbacks. They can usually complement each other. Many research works are trying to integrate some model-based and model-free methods into one algorithm and perform well in simulators or quasi-static robot tasks. Difficulties still exist when algorithms are used in particular trajectory learning tasks. In this paper, we propose a robot trajectory learning framework for precise tasks with discontinuous dynamics and high speed. The trajectories learned from the human demonstration are optimized by DDP and PoWER successively. The framework is tested on the Kendama manipulation task, which can also be difficult for humans to achieve. The results show that our approach can plan the trajectories to successfully complete the task.