关于l_1均值和方差滤波

Constrained Maximum Correntropy Adaptive Filtering

Constrained adaptive filtering algorithms inculding constrained least mean square (CLMS), constrained affine projection (CAP) and constrained recursive least squares (CRLS) have been extensively studied in many applications. Most existing constrained adaptive filtering algorithms are developed under mean square error (MSE) criterion, which is an ideal optimality criterion under Gaussian noises. This assumption however fails to model the behavior of non-Gaussian noises found in practice. Motivated by the robustness and simplicity of maximum correntropy criterion (MCC) in non-Gaussian impulsive …

一类全变差正则化估计问题的ADMM算法

An ADMM Algorithm for a Class of Total Variation Regularized Estimation Problems

我们提出了一个交替增广拉格朗日方法的凸优化问题的成本函数是两项的总和，一个是可分离的可变块，和第二个是可分离的连续可变块之间的差异。这类问题的例子包括融合套索估计，总变差去噪，多期投资组合优化与交易成本。在我们的方法的每次迭代中，第一步涉及对每个变量块进行单独优化，这可以并行进行。第二步在变量上是不可分离的，但可以非常有效地进行。我们将该算法应用于基于均值变化（l_1均值滤波）或方差变化（l_1方差滤波）的数据分割。在一个数值示例中，我们表明，与通用优化求解器SDPT 3相比，我们的实现速度约快10000倍。

Dynamic Clustering Algorithms via Small-Variance Analysis of Markov Chain Mixture Models

Bayesian nonparametrics are a class of probabilistic models in which the model size is inferred from data. A recently developed methodology in this field is small-variance asymptotic analysis, a mathematical technique for deriving learning algorithms that capture much of the flexibility of Bayesian nonparametric inference algorithms, but are simpler to implement and less computationally expensive. Past work on small-variance analysis of Bayesian nonparametric inference algorithms has exclusively considered batch models trained on a single, static dataset, which are incapable of capturing time …

Outlier-Insensitive Kalman Filtering Using NUV Priors

The Kalman filter (KF) is a widely-used algorithm for tracking the latent state of a dynamical system from noisy observations. For systems that are well-described by linear Gaussian state space models, the KF minimizes the mean-squared error (MSE). However, in practice, observations are corrupted by outliers, severely impairing the KFs performance. In this work, an outlier-insensitive KF is proposed, where robustness is achieved by modeling each potential outlier as a normally distributed random variable with unknown variance (NUV). The NUVs variances are estimated online, using both expectati…

对Hierarchical Gaussian Filtering的鲁棒波动更新

Robust volatility updates for Hierarchical Gaussian Filtering

本文提出一种改进的二次近似方法，用于解决HGF网络中波动耦合节点的变分能量问题，避免后验精度为负数导致的计算错误，提升模型鲁棒性。

一种用于实时无人机地形跟随的残差方差匹配递归最小二乘滤波器

A Residual Variance Matching Recursive Least Squares Filter for Real-time UAV Terrain Following

本文提出了一种残差方差匹配递归最小二乘滤波器，用于提升无人机在 wildfire 巡逻中的实时航点估计精度，实验显示其在多个指标上提升了约88%的精度。

非高斯Levy噪声下的状态估计：一种改进的Kalman滤波方法

State estimation under non-Gaussian Levy noise: A modified Kalman filtering method

卡尔曼滤波器广泛用于高斯噪声下线性系的状态估计。当存在非高斯Lévy噪声时，由于非高斯Lévy噪声可能具有无穷大方差的事实，常规卡尔曼滤波器可能失效。针对非高斯Lévy噪声下的线性系设计了一种改进的Kalman滤波器。它以合理的计算成本有效地工作。仿真结果说明了这种非高斯滤波方法。

Bayesian filtering unifies adaptive and non-adaptive neural network optimization methods

We formulate the problem of neural network optimization as Bayesian filtering, where the observations are the backpropagated gradients. While neural network optimization has previously been studied using natural gradient methods which are closely related to Bayesian inference, they were unable to recover standard optimizers such as Adam and RMSprop with a root-mean-square gradient normalizer, instead getting a mean-square normalizer. To recover the root-mean-square normalizer, we find it necessary to account for the temporal dynamics of all the other parameters as they are geing optimized. The…

Kernel Mean Estimation via Spectral Filtering

The problem of estimating the kernel mean in a reproducing kernel Hilbert space (RKHS) is central to kernel methods in that it is used by classical approaches (e.g., when centering a kernel PCA matrix), and it also forms the core inference step of modern kernel methods (e.g., kernel-based non-parametric tests) that rely on embedding probability distributions in RKHSs. Muandet et al. (2014) has shown that shrinkage can help in constructing "better" estimators of the kernel mean than the empirical estimator. The present paper studies the consistency and admissibility of the estimators in Muandet…

Thompson Sampling Algorithms for Mean-Variance Bandits

The multi-armed bandit (MAB) problem is a classical learning task that exemplifies the exploration-exploitation tradeoff. However, standard formulations do not take into account {\em risk}. In online decision making systems, risk is a primary concern. In this regard, the mean-variance risk measure is one of the most common objective functions. Existing algorithms for mean-variance optimization in the context of MAB problems have unrealistic assumptions on the reward distributions. We develop Thompson Sampling-style algorithms for mean-variance MAB and provide comprehensive regret analyses for …