740 research outputs found

    LIPIcs, Volume 251, ITCS 2023, Complete Volume

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    LIPIcs, Volume 251, ITCS 2023, Complete Volum

    Agnostic proper learning of monotone functions: beyond the black-box correction barrier

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    We give the first agnostic, efficient, proper learning algorithm for monotone Boolean functions. Given 2O~(n/ε)2^{\tilde{O}(\sqrt{n}/\varepsilon)} uniformly random examples of an unknown function f:{±1}n{±1}f:\{\pm 1\}^n \rightarrow \{\pm 1\}, our algorithm outputs a hypothesis g:{±1}n{±1}g:\{\pm 1\}^n \rightarrow \{\pm 1\} that is monotone and (opt+ε)(\mathrm{opt} + \varepsilon)-close to ff, where opt\mathrm{opt} is the distance from ff to the closest monotone function. The running time of the algorithm (and consequently the size and evaluation time of the hypothesis) is also 2O~(n/ε)2^{\tilde{O}(\sqrt{n}/\varepsilon)}, nearly matching the lower bound of Blais et al (RANDOM '15). We also give an algorithm for estimating up to additive error ε\varepsilon the distance of an unknown function ff to monotone using a run-time of 2O~(n/ε)2^{\tilde{O}(\sqrt{n}/\varepsilon)}. Previously, for both of these problems, sample-efficient algorithms were known, but these algorithms were not run-time efficient. Our work thus closes this gap in our knowledge between the run-time and sample complexity. This work builds upon the improper learning algorithm of Bshouty and Tamon (JACM '96) and the proper semiagnostic learning algorithm of Lange, Rubinfeld, and Vasilyan (FOCS '22), which obtains a non-monotone Boolean-valued hypothesis, then ``corrects'' it to monotone using query-efficient local computation algorithms on graphs. This black-box correction approach can achieve no error better than 2opt+ε2\mathrm{opt} + \varepsilon information-theoretically; we bypass this barrier by a) augmenting the improper learner with a convex optimization step, and b) learning and correcting a real-valued function before rounding its values to Boolean. Our real-valued correction algorithm solves the ``poset sorting'' problem of [LRV22] for functions over general posets with non-Boolean labels

    Trivial Automorphisms of Reduced Products

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    We introduce a general method for showing under weak forcing axioms that reduced products of countable models of a theory TT have as few automorphisms as possible. We show that such forcing axioms imply that reduced products of countably infinite or finite fields, linear orders, trees, or random graphs have only trivial automorphisms.Comment: 36 page

    Proper conflict-free list-coloring, odd minors, subdivisions, and layered treewidth

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    Proper conflict-free coloring is an intermediate notion between proper coloring of a graph and proper coloring of its square. It is a proper coloring such that for every non-isolated vertex, there exists a color appearing exactly once in its (open) neighborhood. Typical examples of graphs with large proper conflict-free chromatic number include graphs with large chromatic number and bipartite graphs isomorphic to the 11-subdivision of graphs with large chromatic number. In this paper, we prove two rough converse statements that hold even in the list-coloring setting. The first is for sparse graphs: for every graph HH, there exists an integer cHc_H such that every graph with no subdivision of HH is (properly) conflict-free cHc_H-choosable. The second applies to dense graphs: every graph with large conflict-free choice number either contains a large complete graph as an odd minor or contains a bipartite induced subgraph that has large conflict-free choice number. These give two incomparable (partial) answers of a question of Caro, Petru\v{s}evski and \v{S}krekovski. We also prove quantitatively better bounds for minor-closed families, implying some known results about proper conflict-free coloring and odd coloring in the literature. Moreover, we prove that every graph with layered treewidth at most ww is (properly) conflict-free (8w1)(8w-1)-choosable. This result applies to (g,k)(g,k)-planar graphs, which are graphs whose coloring problems have attracted attention recently.Comment: Hickingbotham recently independently announced a paper (arXiv:2203.10402) proving a result similar to the ones in this paper. Please see the notes at the end of this paper for details. v2: add results for odd minors, which applies to graphs with unbounded degeneracy, and change the title of the pape

    Behavior quantification as the missing link between fields: Tools for digital psychiatry and their role in the future of neurobiology

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    The great behavioral heterogeneity observed between individuals with the same psychiatric disorder and even within one individual over time complicates both clinical practice and biomedical research. However, modern technologies are an exciting opportunity to improve behavioral characterization. Existing psychiatry methods that are qualitative or unscalable, such as patient surveys or clinical interviews, can now be collected at a greater capacity and analyzed to produce new quantitative measures. Furthermore, recent capabilities for continuous collection of passive sensor streams, such as phone GPS or smartwatch accelerometer, open avenues of novel questioning that were previously entirely unrealistic. Their temporally dense nature enables a cohesive study of real-time neural and behavioral signals. To develop comprehensive neurobiological models of psychiatric disease, it will be critical to first develop strong methods for behavioral quantification. There is huge potential in what can theoretically be captured by current technologies, but this in itself presents a large computational challenge -- one that will necessitate new data processing tools, new machine learning techniques, and ultimately a shift in how interdisciplinary work is conducted. In my thesis, I detail research projects that take different perspectives on digital psychiatry, subsequently tying ideas together with a concluding discussion on the future of the field. I also provide software infrastructure where relevant, with extensive documentation. Major contributions include scientific arguments and proof of concept results for daily free-form audio journals as an underappreciated psychiatry research datatype, as well as novel stability theorems and pilot empirical success for a proposed multi-area recurrent neural network architecture.Comment: PhD thesis cop

    GPT Semantic Networking: A Dream of the Semantic Web – The Time is Now

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    The book presents research and practical implementations related to natural language processing (NLP) technologies based on the concept of artificial intelligence, generative AI, and the concept of Complex Networks aimed at creating Semantic Networks. The main principles of NLP, training models on large volumes of text data, new universal and multi-purpose language processing systems are presented. It is shown how the combination of NLP and Semantic Networks technologies opens up new horizons for text analysis, context understanding, the formation of domain models, causal networks, etc. This book presents methods for creating Semantic Networks based on prompt engineering. Practices are presented that will help build semantic networks capable of solving complex problems and making revolutionary changes in the analytical activity. The publication is intended for those who are going to use large language models for the construction and analysis of semantic networks in order to solve applied problems, in particular, in the field of decision making.У книзі представлені дослідження та практичні реалізації технологій обробки природної мови (НЛП), заснованих на концепції штучного інтелект, генеративний ШІ та концепція складних мереж, спрямована на створення семантичних мереж. Представлено основні принципи НЛП, моделі навчання на великих обсягах текстових даних, нові універсальні та багатоцільові системи обробки мови. Показано, як поєднання технологій NLP і семантичних мереж відкриває нові горизонти для аналізу тексту, розуміння контексту, формування моделей домену, причинно-наслідкових мереж тощо. У цій книзі представлені методи створення семантичних мереж на основі оперативного проектування. Представлені практики, які допоможуть побудувати семантичні мережі, здатні вирішувати складні проблеми та вносити революційні зміни в аналітичну діяльність. Видання розраховане на тих, хто збирається використовувати велику мову моделі побудови та аналізу семантичних мереж з метою вирішення прикладних задач, зокрема, у сфері прийняття рішень

    Disinformation and Fact-Checking in Contemporary Society

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    Funded by the European Media and Information Fund and research project PID2022-142755OB-I00

    LIPIcs, Volume 261, ICALP 2023, Complete Volume

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    LIPIcs, Volume 261, ICALP 2023, Complete Volum

    Asymptotics for Palette Sparsification

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    It is shown that the following holds for each ε>0\varepsilon>0. For GG an nn-vertex graph of maximum degree DD and "lists" LvL_v (vV(G)v \in V(G)) chosen independently and uniformly from the ((1+ε)lnn(1+\varepsilon)\ln n)-subsets of {1,...,D+1}\{1, ..., D+1\}, G admits a proper coloring σ with σvLvv G \text{ admits a proper coloring } \sigma \text{ with } \sigma_v \in L_v \forall v with probability tending to 1 as DD \to \infty. This is an asymptotically optimal version of a recent "palette sparsification" theorem of Assadi, Chen, and Khanna.Comment: 29 page
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