Case-Based Reasoning

Learning Nearest Neighbor Graphs from Noisy Distance Samples

We consider the problem of learning the nearest neighbor graph of a dataset of n items. The metric is unknown, but we can query an oracle to obtain a noisy estimate of the distance between any pair of items. This framework applies to problem domains where one wants to learn people's preferences from responses commonly modeled as noisy distance judgments. In this paper, we propose an active algorithm to find the graph with high probability and analyze its query complexity. In contrast to existing work that forces Euclidean structure, our method is valid for general metrics, assuming only symmetry and the triangle inequality. Furthermore, we demonstrate efficiency of our method empirically and theoretically, needing only O(n log(n)Delta^-2) queries in favorable settings, where Delta^-2 accounts for the effect of noise. Using crowd-sourced data collected for a subset of the UT Zappos50K dataset, we apply our algorithm to learn which shoes people believe are most similar and show that it beats both an active baseline and ordinal embedding.

Approaching Adaptation Guided Retrieval in Case-Based Reasoning through Inference in Undirected Graphical Models

In Case-Based Reasoning, when the similarity assumption does not hold, the retrieval of a set of cases structurally similar to the query does not guarantee to get a reusable or revisable solution. Knowledge about the adaptability of solutions has to be exploited, in order to define a method for adaptation-guided retrieval. We propose a novel approach to address this problem, where knowledge about the adaptability of the solutions is captured inside a metric Markov Random Field (MRF). Nodes of the MRF represent cases and edges connect nodes whose solutions are close in the solution space. States of the nodes represent different adaptation levels with respect to the potential query. Metric-based potentials enforce connected nodes to share the same state, since cases having similar solutions should have the same adaptability level with respect to the query. The main goal is to enlarge the set of potentially adaptable cases that are retrieved without significantly sacrificing the precision and accuracy of retrieval. We will report on some experiments concerning a retrieval architecture where a simple kNN retrieval (on the problem description) is followed by a further retrieval step based on MRF inference.

Similarity Measure Development for Case-Based Reasoning- A Data-driven Approach

In this paper, we demonstrate a data-driven methodology for modelling the local similarity measures of various attributes in a dataset. We analyse the spread in the numerical attributes and estimate their distribution using polynomial function to showcase an approach for deriving strong initial value ranges of numerical attributes and use a non-overlapping distribution for categorical attributes such that the entire similarity range [0,1] is utilized. We use an open source dataset for demonstrating modelling and development of the similarity measures and will present a case-based reasoning (CBR) system that can be used to search for the most relevant similar cases.

The Twin-System Approach as One Generic Solution for XAI: An Overview of ANN-CBR Twins for Explaining Deep Learning

The notion of twin systems is proposed to address the eXplainable AI (XAI) problem, where an uninterpretable black-box system is mapped to a white-box 'twin' that is more interpretable. In this short paper, we overview very recent work that advances a generic solution to the XAI problem, the so called twin system approach. The most popular twinning in the literature is that between an Artificial Neural Networks (ANN ) as a black box and Case Based Reasoning (CBR) system as a white-box, where the latter acts as an interpretable proxy for the former. We outline how recent work reviving this idea has applied it to deep learning methods. Furthermore, we detail the many fruitful directions in which this work may be taken; such as, determining the most (i) accurate feature-weighting methods to be used, (ii) appropriate deployments for explanatory cases, (iii) useful cases of explanatory value to users.

How Case Based Reasoning Explained Neural Networks: An XAI Survey of Post-Hoc Explanation-by-Example in ANN-CBR Twins

This paper proposes a theoretical analysis of one approach to the eXplainable AI (XAI) problem, using post-hoc explanation-by-example, that relies on the twinning of artificial neural networks (ANNs) with case-based reasoning (CBR) systems; so-called ANN-CBR twins. It surveys these systems to advance a new theoretical interpretation of previous work and define a road map for CBR's further role in XAI. A systematic survey of 1102 papers was conducted to identify a fragmented literature on this topic and trace its influence to more recent work involving deep neural networks (DNNs). The twin-system approach is advanced as one possible coherent, generic solution to the XAI problem. The paper concludes by road-mapping future directions for this XAI solution, considering (i) further tests of feature-weighting techniques, (ii) how explanatory cases might be deployed (e.g., in counterfactuals, a fortori cases), and (iii) the unwelcome, much-ignored issue of user evaluation.

Derived Codebooks for High-Accuracy Nearest Neighbor Search

High-dimensional Nearest Neighbor (NN) search is central in multimedia search systems. Product Quantization (PQ) is a widespread NN search technique which has a high performance and good scalability. PQ compresses high-dimensional vectors into compact codes thanks to a combination of quantizers. Large databases can, therefore, be stored entirely in RAM, enabling fast responses to NN queries. In almost all cases, PQ uses 8-bit quantizers as they offer low response times. In this paper, we advocate the use of 16-bit quantizers. Compared to 8-bit quantizers, 16-bit quantizers boost accuracy but they increase response time by a factor of 3 to 10. We propose a novel approach that allows 16-bit quantizers to offer the same response time as 8-bit quantizers, while still providing a boost of accuracy. Our approach builds on two key ideas: (i) the construction of derived codebooks that allow a fast and approximate distance evaluation, and (ii) a two-pass NN search procedure which builds a candidate set using the derived codebooks, and then refines it using 16-bit quantizers. On 1 billion SIFT vectors, with an inverted index, our approach offers a Recall@100 of 0.85 in 5.2 ms. By contrast, 16-bit quantizers alone offer a Recall@100 of 0.85 in 39 ms, and 8-bit quantizers a Recall@100 of 0.82 in 3.8 ms.

A Theory-Based Evaluation of Nearest Neighbor Models Put Into Practice

In the $k$-nearest neighborhood model ($k$-NN), we are given a set of points $P$, and we shall answer queries $q$ by returning the $k$ nearest neighbors of $q$ in $P$ according to some metric. This concept is crucial in many areas of data analysis and data processing, e.g., computer vision, document retrieval and machine learning. Many $k$-NN algorithms have been published and implemented, but often the relation between parameters and accuracy of the computed $k$-NN is not explicit. We study property testing of $k$-NN graphs in theory and evaluate it empirically: given a point set $P \subset \mathbb{R}^\delta$ and a directed graph $G=(P,E)$, is $G$ a $k$-NN graph, i.e., every point $p \in P$ has outgoing edges to its $k$ nearest neighbors, or is it $\epsilon$-far from being a $k$-NN graph? Here, $\epsilon$-far means that one has to change more than an $\epsilon$-fraction of the edges in order to make $G$ a $k$-NN graph. We develop a randomized algorithm with one-sided error that decides this question, i.e., a property tester for the $k$-NN property, with complexity $O(\sqrt{n} k^2 / \epsilon^2)$ measured in terms of the number of vertices and edges it inspects, and we prove a lower bound of $\Omega(\sqrt{n / \epsilon k})$. We evaluate our tester empirically on the $k$-NN models computed by various algorithms and show that it can be used to detect $k$-NN models with bad accuracy in significantly less time than the building time of the $k$-NN model.

The Nearest Neighbor Information Estimator is Adaptively Near Minimax Rate-Optimal

We analyze the Kozachenko–Leonenko (KL) fixed k-nearest neighbor estimator for the differential entropy. We obtain the first uniform upper bound on its performance for any fixed k over H\"{o}lder balls on a torus without assuming any conditions on how close the density could be from zero. Accompanying a recent minimax lower bound over the H\"{o}lder ball, we show that the KL estimator for any fixed k is achieving the minimax rates up to logarithmic factors without cognizance of the smoothness parameter s of the H\"{o}lder ball for $s \in (0,2]$ and arbitrary dimension d, rendering it the first estimator that provably satisfies this property.

The Nearest Neighbor Information Estimator is Adaptively Near Minimax Rate-Optimal

We analyze the Kozachenko–Leonenko (KL) fixed k-nearest neighbor estimator for the differential entropy. We obtain the first uniform upper bound on its performance for any fixed k over H\"{o}lder balls on a torus without assuming any conditions on how close the density could be from zero. Accompanying a recent minimax lower bound over the H\"{o}lder ball, we show that the KL estimator for any fixed k is achieving the minimax rates up to logarithmic factors without cognizance of the smoothness parameter s of the H\"{o}lder ball for $s \in (0,2]$ and arbitrary dimension d, rendering it the first estimator that provably satisfies this property.

Constructing Ontology-Based Cancer Treatment Decision Support System with Case-Based Reasoning

Decision support is a probabilistic and quantitative method designed for modeling problems in situations with ambiguity. Computer technology can be employed to provide clinical decision support and treatment recommendations. The problem of natural language applications is that they lack formality and the interpretation is not consistent. Conversely, ontologies can capture the intended meaning and specify modeling primitives. Disease Ontology (DO) that pertains to cancer's clinical stages and their corresponding information components is utilized to improve the reasoning ability of a decision support system (DSS). The proposed DSS uses Case-Based Reasoning (CBR) to consider disease manifestations and provides physicians with treatment solutions from similar previous cases for reference. The proposed DSS supports natural language processing (NLP) queries. The DSS obtained 84.63% accuracy in disease classification with the help of the ontology.