我们提出了一种惩罚的非参数方法，以使用整流器二次单元（REEND）激活了深层神经网络，以估计不可分割的模型中的分位数回归过程（QRP），并引入了新的惩罚函数，以实施对瓦解回归曲线的非交叉。我们为估计的QRP建立了非反应过量的风险界限，并在轻度平滑度和规律性条件下得出估计的QRP的平均综合平方误差。为了建立这些非反应风险和估计误差范围，我们还使用$ s> 0 $及其衍生物及其衍生物使用所需的激活的神经网络开发了一个新的错误，用于近似$ c^s $平滑功能。这是必需网络的新近似结果，并且具有独立的兴趣，并且可能在其他问题中有用。我们的数值实验表明，所提出的方法具有竞争性或胜过两种现有方法，包括使用再现核和随机森林的方法，用于非参数分位数回归。

条件分布是描述响应与预测因子之间关系的基本数量。我们提出了一种学习条件分布的Wasserstein生成方法。所提出的方法使用条件发生器将已知分布转换为目标条件分布。通过匹配涉及条件发生器和目标关节分布的联合分布估计条件发生器，使用Wassersein距离作为这些关节分布的差异测量。我们建立了所提出的方法产生的条件采样分布的非渐近误差，并表明它能够减轻维度的诅咒，假设数据分布被支持在低维集上。我们进行数值实验以验证提出的方法，并将其应用于条件采样生成，非参数条件密度估计，预测不确定性量化，二抗体响应数据，图像重构和图像生成的应用。

在本文中，我们考虑从噪声损坏的$ M $二进制测量恢复$ N $尺寸信号，并在假设目标信号具有低生成内在尺寸，即，目标信号可以通过$ l近似生成。$ -lipschitz生成器$ g：\ mathbb {r} ^ k \ lightarrow \ mathbb {r} ^ {n}，k \ ll n $。虽然二进制测量模型是高度非线性的，但我们提出了最小二乘解码器并证明，最多可达$ C $，具有很高的概率，最小二乘解码器实现了急剧估计错误$ \ Mathcal {O}（\ SQRT {只要$ m \ geq \ mathcal {o}（k \ log（ln））$，只要$ m \ geq \ mathcal {o}广泛的数值模拟和具有最先进方法的比较显示了最小的方形解码器对噪声和标志翻转是强大的，如我们的理论所示。通过用正确选择的深度和宽度构造Relu网络，我们验证了（大约）的深生成点，这是独立的兴趣。

在这项工作中，我们将该算法考虑到（非线性）回归问题与$ \ ell_0 $罚款。用于$ \ ell_0 $基于$的优化问题的现有算法通常用固定的步长进行，并且选择适当的步长度取决于限制的强凸性和损耗功能的平滑度，因此难以计算计算。在Sprite的支持检测和根查找\ Cite {HJK2020}的思想中，我们提出了一种新颖且有效的数据驱动线搜索规则，以自适应地确定适当的步长。我们证明了绑定到所提出的算法的$ \ ell_2 $ error，而没有限制成本函数。在线性和逻辑回归问题中具有最先进的算法的大量数值比较显示了所提出的算法的稳定性，有效性和优越性。

在本文中，我们用relu，正弦和$ 2^x $构建神经网络作为激活功能。对于$ [0,1]^d $定义的一般连续$ f $，带有连续模量$ \ omega_f（\ cdot）$，我们构造了Relu-sine- $ 2^x $网络，这些网络享受近似值$ \ MATHCAL {o }（\ omega_f（\ sqrt {d}）\ cdot2^{ - m}+\ omega_ {f} \ in \ Mathbb {n}^{+} $表示与网络宽度相关的超参数。结果，我们可以构建Relu-Sine- $ 2^x $网络，其深度为$ 5 $和宽度$ \ max \ left \ weft \ {\ left \ lceil2d^{3/2} \ left（\ frac {3 \ mu}） {\ epsilon} \ right）^{1/{\ alpha}} \ right \ rceil，2 \ left \ lceil \ log_2 \ frac {3 \ mu d^{\ alpha/2}} \ rceil+2 \ right \} $ tht \ Mathcal {h} _ {\ mu}^{\ alpha}（[0,1]^d）$近似$ f \以$ l^p $ norm $ p \在[1，\ infty）$中的测量，其中$ \ mathcal {h} _ {\ mu}^{\ alpha}（\ alpha}（[0,1]^d）$表示H \“ $ [0,1]^d $定义的旧连续函数类，带有订单$ \ alpha \ in（0,1] $和常数$ \ mu> 0 $。因此，relu-sine- $ 2^x $网络克服了$ \ Mathcal {h} _ {\ mu}^{\ alpha}（[0,1]^d）$。除了其晚餐表达能力外，由relu-sine- $ 2实施的功能，也克服了维度的诅咒。 ^x $网络是（广义）可区分的，使我们能够将SGD应用于训练。

监督表示学习的目标是为预测构建有效的数据表示。在高维复杂数据的理想非参数表示的所有特征中，充分性，低维度和脱离是最重要的。我们提出了一种深层缩小方法，以使用这些特征来学习表示表示。提出的方法是对足够降低方法的非参数概括。我们制定理想的表示学习任务是找到非参数表示，该任务最小化了表征条件独立性并促进人口层面的分离的目标函数。然后，我们使用深层神经网络在非参数上估计样品级别的目标表示。我们表明，估计的深度非参数表示是一致的，因为它的过剩风险会收敛到零。我们使用模拟和真实基准数据的广泛数值实验表明，在分类和回归的背景下，所提出的方法比现有的几种降低方法和标准深度学习模型具有更好的性能。

Embedding words in vector space is a fundamental first step in state-of-the-art natural language processing (NLP). Typical NLP solutions employ pre-defined vector representations to improve generalization by co-locating similar words in vector space. For instance, Word2Vec is a self-supervised predictive model that captures the context of words using a neural network. Similarly, GLoVe is a popular unsupervised model incorporating corpus-wide word co-occurrence statistics. Such word embedding has significantly boosted important NLP tasks, including sentiment analysis, document classification, and machine translation. However, the embeddings are dense floating-point vectors, making them expensive to compute and difficult to interpret. In this paper, we instead propose to represent the semantics of words with a few defining words that are related using propositional logic. To produce such logical embeddings, we introduce a Tsetlin Machine-based autoencoder that learns logical clauses self-supervised. The clauses consist of contextual words like "black," "cup," and "hot" to define other words like "coffee," thus being human-understandable. We evaluate our embedding approach on several intrinsic and extrinsic benchmarks, outperforming GLoVe on six classification tasks. Furthermore, we investigate the interpretability of our embedding using the logical representations acquired during training. We also visualize word clusters in vector space, demonstrating how our logical embedding co-locate similar words.

Model bias triggered by long-tailed data has been widely studied. However, measure based on the number of samples cannot explicate three phenomena simultaneously: (1) Given enough data, the classification performance gain is marginal with additional samples. (2) Classification performance decays precipitously as the number of training samples decreases when there is insufficient data. (3) Model trained on sample-balanced datasets still has different biases for different classes. In this work, we define and quantify the semantic scale of classes, which is used to measure the feature diversity of classes. It is exciting to find experimentally that there is a marginal effect of semantic scale, which perfectly describes the first two phenomena. Further, the quantitative measurement of semantic scale imbalance is proposed, which can accurately reflect model bias on multiple datasets, even on sample-balanced data, revealing a novel perspective for the study of class imbalance. Due to the prevalence of semantic scale imbalance, we propose semantic-scale-balanced learning, including a general loss improvement scheme and a dynamic re-weighting training framework that overcomes the challenge of calculating semantic scales in real-time during iterations. Comprehensive experiments show that dynamic semantic-scale-balanced learning consistently enables the model to perform superiorly on large-scale long-tailed and non-long-tailed natural and medical datasets, which is a good starting point for mitigating the prevalent but unnoticed model bias.

Tsetlin Machine (TM) has been gaining popularity as an inherently interpretable machine leaning method that is able to achieve promising performance with low computational complexity on a variety of applications. The interpretability and the low computational complexity of the TM are inherited from the Boolean expressions for representing various sub-patterns. Although possessing favorable properties, TM has not been the go-to method for AI applications, mainly due to its conceptual and theoretical differences compared with perceptrons and neural networks, which are more widely known and well understood. In this paper, we provide detailed insights for the operational concept of the TM, and try to bridge the gap in the theoretical understanding between the perceptron and the TM. More specifically, we study the operational concept of the TM following the analytical structure of perceptrons, showing the resemblance between the perceptrons and the TM. Through the analysis, we indicated that the TM's weight update can be considered as a special case of the gradient weight update. We also perform an empirical analysis of TM by showing the flexibility in determining the clause length, visualization of decision boundaries and obtaining interpretable boolean expressions from TM. In addition, we also discuss the advantages of TM in terms of its structure and its ability to solve more complex problems.

The stock market prediction has been a traditional yet complex problem researched within diverse research areas and application domains due to its non-linear, highly volatile and complex nature. Existing surveys on stock market prediction often focus on traditional machine learning methods instead of deep learning methods. Deep learning has dominated many domains, gained much success and popularity in recent years in stock market prediction. This motivates us to provide a structured and comprehensive overview of the research on stock market prediction focusing on deep learning techniques. We present four elaborated subtasks of stock market prediction and propose a novel taxonomy to summarize the state-of-the-art models based on deep neural networks from 2011 to 2022. In addition, we also provide detailed statistics on the datasets and evaluation metrics commonly used in the stock market. Finally, we highlight some open issues and point out several future directions by sharing some new perspectives on stock market prediction.