Time series modeling is a well-established problem, which often requires that
methods (1) expressively represent complicated dependencies, (2) forecast long
horizons, and (3) efficiently train over long sequences. State-space models
(SSMs) are classical models for time series, and prior works combine SSMs with
deep learning layers for efficient sequence modeling. However, we find
fundamental limitations with these prior approaches, proving their SSM
representations cannot express autoregressive time series processes. We thus
introduce SpaceTime, a new state-space time series architecture that improves
all three criteria. For expressivity, we propose a new SSM parameterization
based on the companion matrix -- a canonical representation for discrete-time
processes -- which enables SpaceTime's SSM layers to learn desirable
autoregressive processes. For long horizon forecasting, we introduce a
"closed-loop" variation of the companion SSM, which enables SpaceTime to
predict many future time-steps by generating its own layer-wise inputs. For
efficient training and inference, we introduce an algorithm that reduces the
memory and compute of a forward pass with the companion matrix. With sequence
length $\ell$ and state-space size $d$, we go from $\tilde{O}(d \ell)$
naïvely to $\tilde{O}(d + \ell)$. In experiments, our contributions lead to
state-of-the-art results on extensive and diverse benchmarks, with best or
second-best AUROC on 6 / 7 ECG and speech time series classification, and best
MSE on 14 / 16 Informer forecasting tasks. Furthermore, we find SpaceTime (1)
fits AR($p$) processes that prior deep SSMs fail on, (2) forecasts notably more
accurately on longer horizons than prior state-of-the-art, and (3) speeds up
training on real-world ETTh1 data by 73% and 80% relative wall-clock time over
Transformers and LSTMs.

提出了一种名为 SpaceTime 的新型状态空间时间序列体系结构，其通过一种新的 SSM 参数化基于伴随矩阵来提高表现力，并引入一个 “闭环” 变化的伴随 SSM，使其能够生成自己的逐层输入进行长期预测，同时通过算法实现前向传递的内存和计算效率提高，并在大量不同的基准测试中取得最先进的结果。

利用简单的离散状态空间有效建模时间序列

Effectively Modeling Time Series with Simple Discrete State Spaces

In recent years, marked temporal point processes (MTPPs) have emerged as a
powerful modeling machinery to characterize asynchronous events in a wide
variety of applications. MTPPs have demonstrated significant potential in
predicting event-timings, especially for events arriving in near future.
However, due to current design choices, MTPPs often show poor predictive
performance at forecasting event arrivals in distant future. To ameliorate this
limitation, in this paper, we design DualTPP which is specifically well-suited
to long horizon event forecasting. DualTPP has two components. The first
component is an intensity free MTPP model, which captures microscopic or
granular level signals of the event dynamics by modeling the time of future
events. The second component takes a different dual perspective of modeling
aggregated counts of events in a given time-window, thus encapsulating
macroscopic event dynamics. Then we develop a novel inference framework jointly
over the two models % for efficiently forecasting long horizon events by
solving a sequence of constrained quadratic optimization problems. Experiments
with a diverse set of real datasets show that DualTPP outperforms existing MTPP
methods on long horizon forecasting by substantial margins, achieving almost an
order of magnitude reduction in Wasserstein distance between actual events and
forecasts.

本文提出 DualTPP 模型来改善 目前设计选择所带来的远期事件预测效果差的限制，该模型包括两个组件：一个无强度的 MTPP 模型（捕获未来事件的微观或粒度级信号），以及一个从不同的双重视角模拟聚合事件，因此包含宏观事件动态。通过一种新的推理框架，共同关注这两种模型，可以高效地预测长期事件，实验表明该模型比现有 MTPP 方法在长期预测方面表现更好。