This paper is about a curious phenomenon. Suppose we have a data matrix, which is the superposition of a low-rank component and a sparse component. Can we recover each component individually? We prove that under some suitable assumptions, it is possible to recover both the low-rank and the sparse components exactly by solving a very convenient convex program called Principal Component Pursuit; among all feasible decompositions, simply minimize a weighted combination of the nuclear norm and of the 1 norm. This suggests the possibility of a principled approach to robust principal component analysis since our methodology and results assert that one can recover the principal components of a data matrix even though a positive fraction of its entries are arbitrarily corrupted. This extends to the situation where a fraction of the entries are missing as well. We discuss an algorithm for solving this optimization problem, and present applications in the area of video surveillance, where our methodology allows for the detection of objects in a cluttered background, and in the area of face recognition, where it offers a principled way of removing shadows and specularities in images of faces.

We consider a problem of considerable practical interest: the recovery of a data matrix from a sampling of its entries. Suppose that we observe m entries selected uniformly at random from a matrix M . Can we complete the matrix and recover the entries that we have not seen?We show that one can perfectly recover most low-rank matrices from what appears to be an incomplete set of entries. We prove that if the number m of sampled entries obeys m ≥ C n 1.2 r log n for some positive numerical constant C, then with very high probability, most n × n matrices of rank r can be perfectly recovered by solving a simple convex optimization program. This program finds the matrix with minimum nuclear norm that fits the data. The condition above assumes that the rank is not too large. However, if one replaces the 1.2 exponent with 1.25, then the result holds for all values of the rank. Similar results hold for arbitrary rectangular matrices as well. Our results are connected with the recent literature on compressed sensing, and show that objects other than signals and images can be perfectly reconstructed from very limited information.

This paper considers the model problem of reconstructing an object from incomplete frequency samples. Consider a discrete-time signal f ∈ C N and a randomly chosen set of frequencies Ω of mean size τ N . Is it possible to reconstruct f from the partial knowledge of its Fourier coefficients on the set Ω?A typical result of this paper is as follows: for each M > 0, suppose that f obeysthen with probability at least 1 − O(N −M ), f can be reconstructed exactly as the solution to the ℓ 1 minimization problem min g N −1 t=0 |g(t)|, s.t. ĝ(ω) = f (ω) for all ω ∈ Ω.In short, exact recovery may be obtained by solving a convex optimization problem.We give numerical values for α which depends on the desired probability of success; except for the logarithmic factor, the condition on the size of the support is sharp.The methodology extends to a variety of other setups and higher dimensions. For example, we show how one can reconstruct a piecewise constant (one or two-dimensional) object from incomplete frequency samples-provided that the number of jumps (discontinuities) obeys the condition above-by minimizing other convex functionals such as the total-variation of f .

Practitioners use Hidden Markov Models (HMMs) in different problems for about sixty years. Besides, Conditional Random Fields (CRFs) are an alternative to HMMs and appear in the literature as different and somewhat concurrent models. We propose two contributions. First, we show that basic Linear-Chain CRFs (LC-CRFs), considered as different from the HMMs, are in fact equivalent to them in the sense that for each LC-CRF there exists a HMM - that we specify - whom posterior distribution is identical to the given LC-CRF. Second, we show that it is possible to reformulate the generative Bayesian classifiers Maximum Posterior Mode (MPM) and Maximum a Posteriori (MAP) used in HMMs, as discriminative ones. The last point is of importance in many fields, especially in Natural Language Processing (NLP), as it shows that in some situations dropping HMMs in favor of CRFs was not necessary.

Using a comprehensive sample of 2,585 bankruptcies from 1990 to 2019, we benchmark the performance of various machine learning models in predicting financial distress of publicly traded U.S. firms. We find that gradient boosted trees outperform other models in one-year-ahead forecasts. Variable permutation tests show that excess stock returns, idiosyncratic risk, and relative size are the more important variables for predictions. Textual features derived from corporate filings do not improve performance materially. In a credit competition model that accounts for the asymmetric cost of default misclassification, the survival random forest is able to capture large dollar profits.

The term ``neuromorphic'' refers to systems that are closely resembling the architecture and/or the dynamics of biological neural networks. Typical examples are novel computer chips designed to mimic the architecture of a biological brain, or sensors that get inspiration from, e.g., the visual or olfactory systems in insects and mammals to acquire information about the environment. This approach is not without ambition as it promises to enable engineered devices able to reproduce the level of performance observed in biological organisms -- the main immediate advantage being the efficient use of scarce resources, which translates into low power requirements. The emphasis on low power and energy efficiency of neuromorphic devices is a perfect match for space applications. Spacecraft -- especially miniaturized ones -- have strict energy constraints as they need to operate in an environment which is scarce with resources and extremely hostile. In this work we present an overview of early attempts made to study a neuromorphic approach in a space context at the European Space Agency's (ESA) Advanced Concepts Team (ACT).

When searching for policies, reward-sparse environments often lack sufficient information about which behaviors to improve upon or avoid. In such environments, the policy search process is bound to blindly search for reward-yielding transitions and no early reward can bias this search in one direction or another. A way to overcome this is to use intrinsic motivation in order to explore new transitions until a reward is found. In this work, we use a recently proposed definition of intrinsic motivation, Curiosity, in an evolutionary policy search method. We propose Curiosity-ES, an evolutionary strategy adapted to use Curiosity as a fitness metric. We compare Curiosity with Novelty, a commonly used diversity metric, and find that Curiosity can generate higher diversity over full episodes without the need for an explicit diversity criterion and lead to multiple policies which find reward.

Reduced order modeling methods are often used as a mean to reduce simulation costs in industrial applications. Despite their computational advantages, reduced order models (ROMs) often fail to accurately reproduce complex dynamics encountered in real life applications. To address this challenge, we leverage NeuralODEs to propose a novel ROM correction approach based on a time-continuous memory formulation. Finally, experimental results show that our proposed method provides a high level of accuracy while retaining the low computational costs inherent to reduced models.

生成流动网络（GFLOWNETS）是一种算法家族，用于训练在非均衡目标密度下离散对象的顺序采样器，并已成功用于各种概率建模任务。现有的Gflownets培训目标是国家本地的，或者是过渡的本地，或者在整个采样轨迹上传播奖励信号。我们认为，这些替代方案代表了梯度偏见变化权衡的相反目的，并提出了一种利用这种权衡以减轻其有害影响的方法。受到强化学习的TD（$ \ lambda $）算法的启发，我们介绍了一个subtrajectory Balance或subtb（$ \ lambda $），这是一个GFLOWNET培训目标，可以从不同长度的部分动作子序列中学习。我们表明，SubTB（$ \ lambda $）会在先前研究和新环境中加速采样器的收敛，并在具有更长的动作序列和比以前的可能性更长的环境中培训Gflownets。我们还对随机梯度动力学进行了比较分析，阐明了GFLOWNET训练中的偏差变化权衡以及亚条件平衡的优势。

来自光场的大量空间和角度信息允许开发多种差异估计方法。但是，对光场的获取需要高存储和处理成本，从而限制了该技术在实际应用中的使用。为了克服这些缺点，压缩感应（CS）理论使光学体系结构的开发能够获得单个编码的光场测量。该测量是使用需要高计算成本的优化算法或深神经网络来解码的。从压缩光场进行的传统差异估计方法需要首先恢复整个光场，然后再恢复后处理步骤，从而需要长时间。相比之下，这项工作提出了通过省略传统方法所需的恢复步骤来从单个压缩测量中进行快速差异估计。具体而言，我们建议共同优化用于获取单个编码光场快照和卷积神经网络（CNN）的光学体系结构，以估计差异图。在实验上，提出的方法估计了与使用深度学习方法重建的光场相当的差异图。此外，所提出的方法在训练和推理方面的速度比估计重建光场差异的最佳方法要快20倍。