This paper proposes an extension of regression trees by quadratic unconstrained binary optimization (QUBO). Regression trees are very popular prediction models that are trainable with tabular datasets, but their accuracy is insufficient because the decision rules are too simple. The proposed method extends the decision rules in decision trees to multi-dimensional boundaries. Such an extension is generally unimplementable because of computational limitations, however, the proposed method transforms the training process to QUBO, which enables an annealing machine to solve this problem.
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決策樹(Decision Tree）是在已知各種情況發生概率的基礎上，通過構成決策樹來求取凈現值的期望值大于等于零的概率，評價項目風險，判斷其可行性的決策分析方法，是直觀運用概率分析的一種圖解法。由于這種決策分支畫成圖形很像一棵樹的枝干，故稱決策樹。在機器學習中，決策樹是一個預測模型，他代表的是對象屬性與對象值之間的一種映射關系。Entropy = 系統的凌亂程度，使用算法ID3, C4.5和C5.0生成樹算法使用熵。這一度量是基于信息學理論中熵的概念。
決策樹是一種樹形結構，其中每個內部節點表示一個屬性上的測試，每個分支代表一個測試輸出，每個葉節點代表一種類別。
分類樹（決策樹）是一種十分常用的分類方法。他是一種監管學習，所謂監管學習就是給定一堆樣本，每個樣本都有一組屬性和一個類別，這些類別是事先確定的，那么通過學習得到一個分類器，這個分類器能夠對新出現的對象給出正確的分類。這樣的機器學習就被稱之為監督學習。
We introduce a priori Sobolev-space error estimates for the solution of nonlinear, and possibly parametric, PDEs using Gaussian process and kernel based methods. The primary assumptions are: (1) a continuous embedding of the reproducing kernel Hilbert space of the kernel into a Sobolev space of sufficient regularity; and (2) the stability of the differential operator and the solution map of the PDE between corresponding Sobolev spaces. The proof is articulated around Sobolev norm error estimates for kernel interpolants and relies on the minimizing norm property of the solution. The error estimates demonstrate dimension-benign convergence rates if the solution space of the PDE is smooth enough. We illustrate these points with applications to high-dimensional nonlinear elliptic PDEs and parametric PDEs. Although some recent machine learning methods have been presented as breaking the curse of dimensionality in solving high-dimensional PDEs, our analysis suggests a more nuanced picture: there is a trade-off between the regularity of the solution and the presence of the curse of dimensionality. Therefore, our results are in line with the understanding that the curse is absent when the solution is regular enough.
In this paper, we extend the Discrete Empirical Interpolation Method (DEIM) to the third-order tensor case based on the t-product and use it to select important/ significant lateral and horizontal slices/features. The proposed Tubal DEIM (TDEIM) is investigated both theoretically and numerically. The experimental results show that the TDEIM can provide more accurate approximations than the existing methods. An application of the proposed method to the supervised classification task is also presented.
Over the past decade, polar codes have received significant traction and have been selected as the coding method for the control channel in fifth-generation (5G) wireless communication systems. However, conventional polar codes are reliant solely on binary (2x2) kernels, which restricts their block length to being only powers of 2. In response, multi-kernel (MK) polar codes have been proposed as a viable solution to attain greater code length flexibility. This paper proposes an unrolled architecture for encoding both systematic and non-systematic MK polar codes, capable of high-throughput encoding of codes constructed with binary, ternary (3x3), or binary-ternary mixed kernels. The proposed scheme exhibits an unprecedented level of flexibility by supporting 83 different codes and offering various architectures that provide trade-offs between throughput and resource consumption. The FPGA implementation results demonstrate that a partially-pipelined polar encoder of size N=4096 operating at a frequency of 270 MHz gives a throughput of 1080 Gbps. Additionally, a new compiler implemented in Python is given to automatically generate HDL modules for the desired encoders. By inserting the desired parameters, a designer can simply obtain all the necessary VHDL files for FPGA implementation.
Verifying the robustness of machine learning models against evasion attacks at test time is an important research problem. Unfortunately, prior work established that this problem is NP-hard for decision tree ensembles, hence bound to be intractable for specific inputs. In this paper, we identify a restricted class of decision tree ensembles, called large-spread ensembles, which admit a security verification algorithm running in polynomial time. We then propose a new approach called verifiable learning, which advocates the training of such restricted model classes which are amenable for efficient verification. We show the benefits of this idea by designing a new training algorithm that automatically learns a large-spread decision tree ensemble from labelled data, thus enabling its security verification in polynomial time. Experimental results on publicly available datasets confirm that large-spread ensembles trained using our algorithm can be verified in a matter of seconds, using standard commercial hardware. Moreover, large-spread ensembles are more robust than traditional ensembles against evasion attacks, while incurring in just a relatively small loss of accuracy in the non-adversarial setting.
A surge of interest has emerged in utilizing Transformers in diverse vision tasks owing to its formidable performance. However, existing approaches primarily focus on optimizing internal model architecture designs that often entail significant trial and error with high burdens. In this work, we propose a new paradigm dubbed Decision Stream Calibration that boosts the performance of general Vision Transformers. To achieve this, we shed light on the information propagation mechanism in the learning procedure by exploring the correlation between different tokens and the relevance coefficient of multiple dimensions. Upon further analysis, it was discovered that 1) the final decision is associated with tokens of foreground targets, while token features of foreground target will be transmitted into the next layer as much as possible, and the useless token features of background area will be eliminated gradually in the forward propagation. 2) Each category is solely associated with specific sparse dimensions in the tokens. Based on the discoveries mentioned above, we designed a two-stage calibration scheme, namely ViT-Calibrator, including token propagation calibration stage and dimension propagation calibration stage. Extensive experiments on commonly used datasets show that the proposed approach can achieve promising results. The source codes are given in the supplements.
Decision Trees (DTs) are commonly used for many machine learning tasks due to their high degree of interpretability. However, learning a DT from data is a difficult optimization problem, as it is non-convex and non-differentiable. Therefore, common approaches learn DTs using a greedy growth algorithm that minimizes the impurity locally at each internal node. Unfortunately, this greedy procedure can lead to suboptimal trees. In this paper, we present a novel approach for learning hard, axis-aligned DTs with gradient descent. The proposed method uses backpropagation with a straight-through operator on a dense DT representation to jointly optimize all tree parameters. Our approach outperforms existing methods on binary classification benchmarks and achieves competitive results for multi-class tasks.
Bayesian optimization is a class of global optimization techniques. In Bayesian optimization, the underlying objective function is modeled as a realization of a Gaussian process. Although the Gaussian process assumption implies a random distribution of the Bayesian optimization outputs, quantification of this uncertainty is rarely studied in the literature. In this work, we propose a novel approach to assess the output uncertainty of Bayesian optimization algorithms, which proceeds by constructing confidence regions of the maximum point (or value) of the objective function. These regions can be computed efficiently, and their confidence levels are guaranteed by the uniform error bounds for sequential Gaussian process regression newly developed in the present work. Our theory provides a unified uncertainty quantification framework for all existing sequential sampling policies and stopping criteria.
Gradient-boosted decision trees (GBDT) are widely used and highly effective machine learning approach for tabular data modeling. However, their complex structure may lead to low robustness against small covariate perturbation in unseen data. In this study, we apply one-hot encoding to convert a GBDT model into a linear framework, through encoding of each tree leaf to one dummy variable. This allows for the use of linear regression techniques, plus a novel risk decomposition for assessing the robustness of a GBDT model against covariate perturbations. We propose to enhance the robustness of GBDT models by refitting their linear regression forms with $L_1$ or $L_2$ regularization. Theoretical results are obtained about the effect of regularization on the model performance and robustness. It is demonstrated through numerical experiments that the proposed regularization approach can enhance the robustness of the one-hot-encoded GBDT models.
Deep learning has revolutionized many areas of machine learning, from computer vision to natural language processing, but these high-performance models are generally "black box." Explaining such models would improve transparency and trust in AI-powered decision making and is necessary for understanding other practical needs such as robustness and fairness. A popular means of enhancing model transparency is to quantify how individual inputs contribute to model outputs (called attributions) and the magnitude of interactions between groups of inputs. A growing number of these methods import concepts and results from game theory to produce attributions and interactions. This work presents a unifying framework for game-theory-inspired attribution and $k^\text{th}$-order interaction methods. We show that, given modest assumptions, a unique full account of interactions between features, called synergies, is possible in the continuous input setting. We identify how various methods are characterized by their policy of distributing synergies. We also demonstrate that gradient-based methods are characterized by their actions on monomials, a type of synergy function, and introduce unique gradient-based methods. We show that the combination of various criteria uniquely defines the attribution/interaction methods. Thus, the community needs to identify goals and contexts when developing and employing attribution and interaction methods.
Data transmission between two or more digital devices in industry and government demands secure and agile technology. Digital information distribution often requires deployment of Internet of Things (IoT) devices and Data Fusion techniques which have also gained popularity in both, civilian and military environments, such as, emergence of Smart Cities and Internet of Battlefield Things (IoBT). This usually requires capturing and consolidating data from multiple sources. Because datasets do not necessarily originate from identical sensors, fused data typically results in a complex Big Data problem. Due to potentially sensitive nature of IoT datasets, Blockchain technology is used to facilitate secure sharing of IoT datasets, which allows digital information to be distributed, but not copied. However, blockchain has several limitations related to complexity, scalability, and excessive energy consumption. We propose an approach to hide information (sensor signal) by transforming it to an image or an audio signal. In one of the latest attempts to the military modernization, we investigate sensor fusion approach by investigating the challenges of enabling an intelligent identification and detection operation and demonstrates the feasibility of the proposed Deep Learning and Anomaly Detection models that can support future application for specific hand gesture alert system from wearable devices.
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