Interactive Deep Learning for Shelf Life Prediction of Muskmelons Based on an Active Learning Approach

A pivotal topic in agriculture and food monitoring is the assessment of the quality and ripeness of agricultural products by using non-destructive testing techniques. Acoustic testing offers a rapid in situ analysis of the state of the agricultural good, obtaining global information of its interior. While deep learning (DL) methods have outperformed state-of-the-art benchmarks in various applications, the reason for lacking adaptation of DL algorithms such as convolutional neural networks (CNNs) can be traced back to its high data inefficiency and the absence of annotated data. Active learning is a framework that has been heavily used in machine learning when the labelled instances are scarce or cumbersome to obtain. This is specifically of interest when the DL algorithm is highly uncertain about the label of an instance. By allowing the human-in-the-loop for guidance, a continuous improvement of the DL algorithm based on a sample efficient manner can be obtained. This paper seeks to study the applicability of active learning when grading ‘Galia’ muskmelons based on its shelf life. We propose k-Determinantal Point Processes (k-DPP), which is a purely diversity-based method that allows to take influence on the exploration within the feature space based on the chosen subset k. While getting coequal results to uncertainty-based approaches when k is large, we simultaneously obtain a better exploration of the data distribution. While the implementation based on eigendecomposition takes up a runtime of O(n3), this can further be reduced to O(n·poly(k)) based on rejection sampling. We suggest the use of diversity-based acquisition when only a few labelled samples are available, allowing for better exploration while counteracting the disadvantage of missing the training objective in uncertainty-based methods following a greedy fashion.

Partial isometries, duality, and determinantal point processes

A determinantal point process (DPP) is an ensemble of random nonnegative-integer-valued Radon measures [Formula: see text] on a space [Formula: see text] with measure [Formula: see text], whose correlation functions are all given by determinants specified by an integral kernel [Formula: see text] called the correlation kernel. We consider a pair of Hilbert spaces, [Formula: see text], which are assumed to be realized as [Formula: see text]-spaces, [Formula: see text], [Formula: see text], and introduce a bounded linear operator [Formula: see text] and its adjoint [Formula: see text]. We show that if [Formula: see text] is a partial isometry of locally Hilbert–Schmidt class, then we have a unique DPP [Formula: see text] associated with [Formula: see text]. In addition, if [Formula: see text] is also of locally Hilbert–Schmidt class, then we have a unique pair of DPPs, [Formula: see text], [Formula: see text]. We also give a practical framework which makes [Formula: see text] and [Formula: see text] satisfy the above conditions. Our framework to construct pairs of DPPs implies useful duality relations between DPPs making pairs. For a correlation kernel of a given DPP our formula can provide plural different expressions, which reveal different aspects of the DPP. In order to demonstrate these advantages of our framework as well as to show that the class of DPPs obtained by this method is large enough to study universal structures in a variety of DPPs, we report plenty of examples of DPPs in one-, two- and higher-dimensional spaces [Formula: see text], where several types of weak convergence from finite DPPs to infinite DPPs are given. One-parameter ([Formula: see text]) series of infinite DPPs on [Formula: see text] and [Formula: see text] are discussed, which we call the Euclidean and the Heisenberg families of DPPs, respectively, following the terminologies of Zelditch.

Multi-Document Summarization with Determinantal Point Process Attention

The ability to convey relevant and diverse information is critical in multi-document summarization and yet remains elusive for neural seq-to-seq models whose outputs are often redundant and fail to correctly cover important details. In this work, we propose an attention mechanism which encourages greater focus on relevance and diversity. Attention weights are computed based on (proportional) probabilities given by Determinantal Point Processes (DPPs) defined on the set of content units to be summarized. DPPs have been successfully used in extractive summarisation, here we use them to select relevant and diverse content for neural abstractive summarisation. We integrate DPP-based attention with various seq-to-seq architectures ranging from CNNs to LSTMs, and Transformers. Experimental evaluation shows that our attention mechanism consistently improves summarization and delivers performance comparable with the state-of-the-art on the MultiNews dataset

Couplings for determinantal point processes and their reduced Palm distributions with a view to quantifying repulsiveness

For a determinantal point process (DPP) X with a kernel K whose spectrum is strictly less than one, André Goldman has established a coupling to its reduced Palm process $X^u$ at a point u with $K(u,u)>0$ so that, almost surely, $X^u$ is obtained by removing a finite number of points from X. We sharpen this result, assuming weaker conditions and establishing that $X^u$ can be obtained by removing at most one point from X, where we specify the distribution of the difference $\xi_u: = X\setminus X^u$. This is used to discuss the degree of repulsiveness in DPPs in terms of $\xi_u$, including Ginibre point processes and other specific parametric models for DPPs.