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Rule learning approaches for knowledge graph completion are efficient, interpretable and competitive to purely neural models. The rule aggregation problem is concerned with finding one plausibility score for a candidate fact which was…
The problem of Hadamard quantum coin measurement in $n$ trials, with arbitrary number of repeated consecutive last states is formulated in terms of Fibonacci sequences for duplicated states, Tribonacci numbers for triplicated states and…
Flux ratio `anomalies' in quadruply-imaged gravitational lenses can be explained with galactic substructure of the sort predicted by CDM, but the strength and uniqueness of that hypothesis needs to be further assessed. A good way to do that…
In this paper, we investigate the problem of assessing statistical methods and effectively summarizing results from simulations. Specifically, we consider problems of the type where multiple methods are compared on a reasonably large test…
We give optimal solutions to all versions of the popular counterfeit coin problem obtained by varying whether (i) we know if the counterfeit coin is heavier or lighter than the genuine ones, (ii) we know if the counterfeit coin exists,…
Although a concept class may be learnt more efficiently using quantum samples as compared with classical samples in certain scenarios, Arunachalam and de Wolf (JMLR, 2018) proved that quantum learners are asymptotically no more efficient…
We address the problem of maximizing an unknown submodular function that can only be accessed via noisy evaluations. Our work is motivated by the task of summarizing content, e.g., image collections, by leveraging users' feedback in form of…
We study a relationship between rational proper maps of balls in different dimensions and strongly plurisubharmonic exhaustion functions of the unit ball induced by such maps. Putting the unique critical point of this exhaustion function at…
In view of the problem of image inpainting error continuation and the deviation of finding best match block, an improved Criminisi algorithm is proposed. The improvement was mainly embodied in two aspects. In the repairing order aspect, we…
Stein's (1959) problem highlights the phenomenon called the probability dilution in high dimensional cases, which is known as a fundamental deficiency in probabilistic inference. The satellite conjunction problem also suffers from…
The Coin Change problem, also known as the Change-Making problem, is a well-studied combinatorial optimization problem, which involves minimizing the number of coins needed to make a specific change amount using a given set of coin…
The functions satisfying the mean value property for an n-dimensional cube are determined explicitly. This problem is related to invariant theory for a finite reflection group, especially to a system of invariant differential equations.…
Deep learning-based methods have achieved a breakthrough in image anomaly detection, but their complexity introduces a considerable challenge to understanding why an instance is predicted to be anomalous. We introduce a novel explanation…
Collecting labeled data is costly and thus a critical bottleneck in real-world classification tasks. To mitigate this problem, we propose a novel setting, namely learning from complementary labels for multi-class classification. A…
The Vanilla Power Law Inflation is plagued with two severe drawbacks, the one being the issue of graceful exit, and the other being its compatibility with the existing data. There's yet another daunting problem generic to any inflationary…
The literature on Dedekind sums is vast. In this expository paper we show that there is a common thread to many generalizations of Dedekind sums, namely through the study of lattice point enumeration of rational polytopes. In particular,…
Hyperspectral images provide much more information than conventional imaging techniques, allowing a precise identification of the materials in the observed scene, but because of the limited spatial resolution, the observations are usually…
We introduce several generalizations of classical computer science problems obtained by replacing simpler objective functions with general submodular functions. The new problems include submodular load balancing, which generalizes load…
In recommendation systems, items are likely to be exposed to various users and we would like to learn about the familiarity of a new user with an existing item. This can be formulated as an anomaly detection (AD) problem distinguishing…
With the exception of superselection rules, there are no known explicit violations of the Principle of quantum Superposition. However, quantum measurement and the emergence of classicality seem to imply that the Principle of Superposition…