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Computational Learning Theory


Adiabatic Quantum Optimization Fails to Solve the Knapsack Problem

#artificialintelligence

In this work, we attempt to solve the integer-weight knapsack problem using the D-Wave 2000Q adiabatic quantum computer. The knapsack problem is a well-known NP-complete problem in computer science, with applications in economics, business, finance, etc. We attempt to solve a number of small knapsack problems whose optimal solutions are known; we find that adiabatic quantum optimization fails to produce solutions corresponding to optimal filling of the knapsack in all problem instances. We compare results obtained on the quantum hardware to the classical simulated annealing algorithm and two solvers employing a hybrid branch-and-bound algorithm. The simulated annealing algorithm also fails to produce the optimal filling of the knapsack, though solutions obtained by simulated and quantum annealing are no more similar to each other than to the correct solution.


A Gentle Introduction to Computational Learning Theory - AnalyticsWeek

#artificialintelligence

Computational learning theory, or statistical learning theory, refers to mathematical frameworks for quantifying learning tasks and algorithms. These are sub-fields of machine learning that a machine learning practitioner does not need to know in great depth in order to achieve good results on a wide range of problems. Nevertheless, it is a sub-field where having a high-level understanding of some of the more prominent methods may provide insight into the broader task of learning from data. In this post, you will discover a gentle introduction to computational learning theory for machine learning. A Gentle Introduction to Computational Learning Theory Photo by someone10x, some rights reserved.


A Gentle Introduction to Computational Learning Theory

#artificialintelligence

Computational learning theory, or statistical learning theory, refers to mathematical frameworks for quantifying learning tasks and algorithms. These are sub-fields of machine learning that a machine learning practitioner does not need to know in great depth in order to achieve good results on a wide range of problems. Nevertheless, it is a sub-field where having a high-level understanding of some of the more prominent methods may provide insight into the broader task of learning from data. In this post, you will discover a gentle introduction to computational learning theory for machine learning. A Gentle Introduction to Computational Learning Theory Photo by someone10x, some rights reserved.


Departmental Teaching awards announced

Oxford Comp Sci

Prof. Gavin Lowe Excellent student feedback for teaching Concurrent Programming and Concurrency (with the latter moved to remote teaching during TT 2020).


Categorical anomaly detection in heterogeneous data using minimum description length clustering

arXiv.org Artificial Intelligence

Two examples of anomaly detection based on MDL have been been proposed for categorical data based on the minimum description studied and shown to perform well: the OC3 algorithm [21] based length (MDL) principle. However, they can be ineffective when on an itemset mining technique called Krimp [26], and the CompreX detecting anomalies in heterogeneous datasets representing a mixture algorithm [2]. Broadly speaking, both take a similar approach: of different sources, such as security scenarios in which system first, a model H of the data that compresses it well is found using a and user processes have distinct behavior patterns. We propose a heuristic search, balancing the model complexity L(H) (number of meta-algorithm for enhancing any MDL-based anomaly detection bits required to compress the model structure/parameters) against model to deal with heterogeneous data by fitting a mixture model the data complexity L(X H) (number of bits required to compress to the data, via a variant of k-means clustering. Our experimental the data given the model). Once such a model H is found, we assign results show that using a discrete mixture model provides competitive to each object x X a score corresponding to the object's performance relative to two previous anomaly detection compressed size L(x H) given the selected model. Intuitively, if the algorithms, while mixtures of more sophisticated models yield further model accurately characterizes the data as a whole, records that are gains, on both synthetic datasets and realistic datasets from a representative will compress well, yielding a low anomaly score, security scenario.


Optimal Continual Learning has Perfect Memory and is NP-hard

arXiv.org Artificial Intelligence

Continual Learning (CL) algorithms incrementally learn a predictor or representation across multiple sequentially observed tasks. Designing CL algorithms that perform reliably and avoid so-called catastrophic forgetting has proven a persistent challenge. The current paper develops a theoretical approach that explains why. In particular, we derive the computational properties which CL algorithms would have to possess in order to avoid catastrophic forgetting. Our main finding is that such optimal CL algorithms generally solve an NP-hard problem and will require perfect memory to do so. The findings are of theoretical interest, but also explain the excellent performance of CL algorithms using experience replay, episodic memory and core sets relative to regularization-based approaches.


SAT Heritage: a community-driven effort for archiving, building and running more than thousand SAT solvers

arXiv.org Artificial Intelligence

SAT research has a long history of source code and binary releases, thanks to competitions organized every year. However, since every cycle of competitions has its own set of rules and an adhoc way of publishing source code and binaries, compiling or even running any solver may be harder than what it seems. Moreover, there has been more than a thousand solvers published so far, some of them released in the early 90's. If the SAT community wants to archive and be able to keep track of all the solvers that made its history, it urgently needs to deploy an important effort. We propose to initiate a community-driven effort to archive and to allow easy compilation and running of all SAT solvers that have been released so far. We rely on the best tools for archiving and building binaries (thanks to Docker, GitHub and Zenodo) and provide a consistent and easy way for this. Thanks to our tool, building (or running) a solver from its source (or from its binary) can be done in one line.


Technical Perspective: Algorithm Selection as a Learning Problem

Communications of the ACM

The following paper by Gupta and Roughgarden--"Data-Driven Algorithm Design"--addresses the issue that the best algorithm to use for many problems depends on what the input "looks like." Certain algorithms work better for certain types of inputs, whereas other algorithms work better for others. This is especially the case for NP-hard problems, where we do not expect to ever have algorithms that work well on all inputs: instead, we often have various heuristics that each work better in different settings. Moreover, heuristic strategies often have parameters or hyperparameters that must be set in some way. The authors present a theoretical formulation and analysis of algorithm selection using the well-developed framework of PAC-learning to analyze fundamental learning questions.


Data-Driven Algorithm Design

Communications of the ACM

The best algorithm for a computational problem generally depends on the "relevant inputs," a concept that depends on the application domain and often defies formal articulation. Although there is a large literature on empirical approaches to selecting the best algorithm for a given application domain, there has been surprisingly little theoretical analysis of the problem. Our framework captures several state-of-the-art empirical and theoretical approaches to the problem, and our results identify conditions under which these approaches are guaranteed to perform well. We interpret our results in the contexts of learning greedy heuristics, instance feature-based algorithm selection, and parameter tuning in machine learning. Rigorously comparing algorithms is hard. Two different algorithms for a computational problem generally have incomparable performance: one algorithm is better on some inputs but worse on the others. The simplest and most common solution in the theoretical analysis of algorithms is to summarize the performance of an algorithm using a single number, such as its worst-case performance or its average-case performance with respect to an input distribution. This approach effectively advocates using the algorithm with the best summarizing value (e.g., the smallest worst-case running time). Solving a problem "in practice" generally means identifying an algorithm that works well for most or all instances of interest. When the "instances of interest" are easy to specify formally in advance--say, planar graphs, the traditional analysis approaches often give accurate performance predictions and identify useful algorithms.


Search for developments of a box having multiple ways of folding by SAT solver

arXiv.org Artificial Intelligence

A polyomino is a two-dimensional shape formed by joining unit squares edge to edge. A polyomino is called a development if it can make a box by folding edges of unit squares forming the polyomino. As in Figure 1, there are developments that can fold into two incongruent boxes. Many such developments have been discovered. For example, for the surface area 22, it was shown by an exhaustive computer search that there are 2,263 common developments of two boxes of size 1 1 5 and 1 2 3 [1].