Diffusion models are a remarkably effective way of learning and sampling from
a distribution $p(x)$. In posterior sampling, one is also given a measurement
model $p(y \mid x)$ and a measurement $y$, and would like to sample from $p(x
\mid y)$. Posterior sampling is useful for tasks such as inpainting,
super-resolution, and MRI reconstruction, so a number of recent works have
given algorithms to heuristically approximate it; but none are known to
converge to the correct distribution in polynomial time.
In this paper we show that posterior sampling is \emph{computationally
intractable}: under the most basic assumption in cryptography -- that one-way
functions exist -- there are instances for which \emph{every} algorithm takes
superpolynomial time, even though \emph{unconditional} sampling is provably
fast. We also show that the exponential-time rejection sampling algorithm is
essentially optimal under the stronger plausible assumption that there are
one-way functions that take exponential time to invert.

传播模型、后验抽样、测量模型、修复图像、指数级时间拒绝抽样是本研究的主要关键词及研究领域。

扩散后验抽样的计算难题

Diffusion Posterior Sampling is Computationally Intractable

In the pursuit of further advancement in the field of target tracking, this
paper explores the efficacy of a feedforward neural network in predicting
drones tracks, aiming to eventually, compare the tracks created by the
well-known Kalman filter and the ones created by our proposed neural network.
The unique feature of our proposed neural network tracker is that it is using
only a measurement model to estimate the next states of the track. Object model
selection and linearization is one of the challenges that always face in the
tracking process. The neural network uses a sliding window to incorporate the
history of measurements when applying estimations of the track values. The
testing results are comparable to the ones generated by the Kalman filter,
especially for the cases where there is low measurement covariance. The
complexity of linearization is avoided when using this proposed model.

本研究探讨了使用前馈神经网络在目标跟踪领域中的有效性，旨在比较由 Kalman 滤波器和我们提出的神经网络创建的轨迹。我们提出的神经网络跟踪器的独特功能是它仅使用测量模型来估计轨迹的下一个状态，并在应用轨迹值的估计时使用滑动窗口来合并测量历史记录，避免了线性化的复杂性。

基于测量模型的滑动窗口神经生成跟踪

Sliding Window Neural Generated Tracking Based on Measurement Model

We establish conditions under which latent causal graphs are
nonparametrically identifiable and can be reconstructed from unknown
interventions in the latent space. Our primary focus is the identification of
the latent structure in a measurement model, i.e. causal graphical models where
dependence between observed variables is insignificant compared to dependence
between latent representations, without making parametric assumptions such as
linearity or Gaussianity. Moreover, we do not assume the number of hidden
variables is known, and we show that at most one unknown intervention per
hidden variable is needed. This extends a recent line of work on learning
causal representations from observations and interventions. The proofs are
constructive and introduce two new graphical concepts -- imaginary subsets and
isolated edges -- that may be useful in their own right. As a matter of
independent interest, the proofs also involve a novel characterization of the
limits of edge orientations within the equivalence class of DAGs induced by
unknown interventions. Experiments confirm that the latent graph can be
recovered from data using our theoretical results. These are the first results
to characterize the conditions under which causal representations are
identifiable without making any parametric assumptions in a general setting
with unknown interventions and without faithfulness.

本文介绍了一种在潜在空间中通过未知干预重建潜在因果图的方法，不需要进行参数假设，并且不需要已知潜在变量的数量，每个潜在变量最多只需要一个未知干预，通过引入虚集和孤立边的两个新图形概念，可构造性地证明了这种方法的可行性。

学习未知干预下非参数潜在因果图

Learning nonparametric latent causal graphs with unknown interventions

High-resolution functional imaging is providing increasingly rich
measurements of brain activity in animals and humans. A major challenge is to
leverage such data to gain insight into the brain's computational mechanisms.
The first step is to define candidate brain-computational models (BCMs) that
can perform the behavioural task in question. We would then like to infer,
which of the candidate BCMs best accounts for measured brain-activity data.
Here we describe a method that complements each BCM by a measurement model
(MM), which simulates the way the brain-activity measurements reflect neuronal
activity (e.g. local averaging in fMRI voxels or sparse sampling in array
recordings). The resulting generative model (BCM-MM) produces simulated
measurements. In order to avoid having to fit the MM to predict each individual
measurement channel of the brain-activity data, we compare the measured and
predicted data at the level of summary statistics. We describe a novel
particular implementation of this approach, called probabilistic RSA (pRSA)
with measurement models, which uses representational dissimilarity matrices
(RDMs) as the summary statistics. We validate this method by simulations of
fMRI measurements (locally averaging voxels) based on a deep convolutional
neural network for visual object recognition. Results indicate that the way the
measurements sample the activity patterns strongly affects the apparent
representational dissimilarities. However, modelling of the measurement process
can account for these effects and different BCMs remain distinguishable even
under substantial noise. The pRSA method enables us to perform Bayesian
inference on the set of BCMs and to recognise the data-generating model in each
case.

本研究提出了使用测量模型对候选的大脑计算模型进行补充并建立生成模型。通过使用表示不相似矩阵作为总结统计数据，可在众多的大脑计算模型中执行贝叶斯推断。