**Abductive Reasoning**

Abductive reasoning (also called abduction, abductive inference, or retroduction) is a form of logical inference which starts with an observation or set of observations then seeks to find the simplest and most likely explanation. In abductive reasoning, unlike in deductive reasoning, the premises do not guarantee the conclusion. One can understand abductive reasoning as inference to the best explanation, although not all uses of the terms abduction and inference to the best explanation are exactly equivalent. In the 1990s, as computing power grew, the fields of law, computer science, and artificial intelligence research spurred renewed interest in the subject of abduction. Diagnostic expert systems frequently employ abduction. … **Evolutionary Attention-based LSTM (EA-LSTM)**

Time series prediction with deep learning methods, especially long short-term memory neural networks (LSTMs), have scored significant achievements in recent years. Despite the fact that the LSTMs can help to capture long-term dependencies, its ability to pay different degree of attention on sub-window feature within multiple time-steps is insufficient. To address this issue, an evolutionary attention-based LSTM training with competitive random search is proposed for multivariate time series prediction. By transferring shared parameters, an evolutionary attention learning approach is introduced to the LSTMs model. Thus, like that for biological evolution, the pattern for importance-based attention sampling can be confirmed during temporal relationship mining. To refrain from being trapped into partial optimization like traditional gradient-based methods, an evolutionary computation inspired competitive random search method is proposed, which can well configure the parameters in the attention layer. Experimental results have illustrated that the proposed model can achieve competetive prediction performance compared with other baseline methods. … **Matrix-Variate Gaussian (MVG)**

Differential privacy mechanism design has traditionally been tailored for a scalar-valued query function. Although many mechanisms such as the Laplace and Gaussian mechanisms can be extended to a matrix-valued query function by adding i.i.d. noise to each element of the matrix, this method is often suboptimal as it forfeits an opportunity to exploit the structural characteristics typically associated with matrix analysis. To address this challenge, we propose a novel differential privacy mechanism called the Matrix-Variate Gaussian (MVG) mechanism, which adds a matrix-valued noise drawn from a matrix-variate Gaussian distribution, and we rigorously prove that the MVG mechanism preserves $(\epsilon,\delta)$-differential privacy. Furthermore, we introduce the concept of directional noise made possible by the design of the MVG mechanism. Directional noise allows the impact of the noise on the utility of the matrix-valued query function to be moderated. Finally, we experimentally demonstrate the performance of our mechanism using three matrix-valued queries on three privacy-sensitive datasets. We find that the MVG mechanism notably outperforms four previous state-of-the-art approaches, and provides comparable utility to the non-private baseline. Our work thus presents a promising prospect for both future research and implementation of differential privacy for matrix-valued query functions. … **Column Subset Selection Problem (CSSP)**

Dimensionality reduction is a first step of many machine learning pipelines. Two popular approaches are principal component analysis, which projects onto a small number of well chosen but non-interpretable directions, and feature selection, which selects a small number of the original features. Feature selection can be abstracted as a numerical linear algebra problem called the column subset selection problem (CSSP). CSSP corresponds to selecting the best subset of columns of a matrix $X \in \mathbb{R}^{N \times d}$, where \emph{best} is often meant in the sense of minimizing the approximation error, i.e., the norm of the residual after projection of $X$ onto the space spanned by the selected columns. Such an optimization over subsets of ${1,\dots,d}$ is usually impractical. One workaround that has been vastly explored is to resort to polynomial-cost, random subset selection algorithms that favor small values of this approximation error. We propose such a randomized algorithm, based on sampling from a projection determinantal point process (DPP), a repulsive distribution over a fixed number $k$ of indices ${1,\dots,d}$ that favors diversity among the selected columns. We give bounds on the ratio of the expected approximation error for this DPP over the optimal error of PCA. These bounds improve over the state-of-the-art bounds of \emph{volume sampling} when some realistic structural assumptions are satisfied for $X$. Numerical experiments suggest that our bounds are tight, and that our algorithms have comparable performance with the \emph{double phase} algorithm, often considered to be the practical state-of-the-art. Column subset selection with DPPs thus inherits the best of both worlds: good empirical performance and tight error bounds. …

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