145,480 research outputs found
Representation Independent Analytics Over Structured Data
Database analytics algorithms leverage quantifiable structural properties of
the data to predict interesting concepts and relationships. The same
information, however, can be represented using many different structures and
the structural properties observed over particular representations do not
necessarily hold for alternative structures. Thus, there is no guarantee that
current database analytics algorithms will still provide the correct insights,
no matter what structures are chosen to organize the database. Because these
algorithms tend to be highly effective over some choices of structure, such as
that of the databases used to validate them, but not so effective with others,
database analytics has largely remained the province of experts who can find
the desired forms for these algorithms. We argue that in order to make database
analytics usable, we should use or develop algorithms that are effective over a
wide range of choices of structural organizations. We introduce the notion of
representation independence, study its fundamental properties for a wide range
of data analytics algorithms, and empirically analyze the amount of
representation independence of some popular database analytics algorithms. Our
results indicate that most algorithms are not generally representation
independent and find the characteristics of more representation independent
heuristics under certain representational shifts
Lifted rule injection for relation embeddings
Methods based on representation learning currently hold the state-of-the-art in many natural language processing and knowledge base inference tasks. Yet, a major challenge is how to efficiently incorporate commonsense knowledge into such models. A recent approach regularizes relation and entity representations by propositionalization of first-order logic rules. However, propositionalization does not scale beyond domains with only few entities and rules. In this paper we present a highly efficient method for incorporating implication rules into distributed representations for automated knowledge base construction. We map entity-tuple embeddings into an approximately Boolean space and encourage a partial ordering over relation embeddings based on implication rules mined from WordNet. Surprisingly, we find that the strong restriction of the entity-tuple embedding space does not hurt the expressiveness of the model and even acts as a regularizer that improves generalization. By incorporating few commonsense rules, we achieve an increase of 2 percentage points mean average precision over a matrix factorization baseline, while observing a negligible increase in runtime
Graph-theoretic strengths of contextuality
Cabello-Severini-Winter and Abramsky-Hardy (building on the framework of
Abramsky-Brandenburger) both provide classes of Bell and contextuality
inequalities for very general experimental scenarios using vastly different
mathematical techniques. We review both approaches, carefully detail the links
between them, and give simple, graph-theoretic methods for finding
inequality-free proofs of nonlocality and contextuality and for finding states
exhibiting strong nonlocality and/or contextuality. Finally, we apply these
methods to concrete examples in stabilizer quantum mechanics relevant to
understanding contextuality as a resource in quantum computation.Comment: 13 pages; significantly rewritte
Objective and Subjective Rationality in a Multiple Prior Model
A decision maker is characterized by two binary relations. The first reflects decisions that are rational in an “objective” sense: the decision maker can convince others that she is right in making them. The second relation models decisions that are rational in a “subjective” sense: the decision maker cannot be convinced that she is wrong in making them. We impose axioms on these relations that allow a joint representation by a single set of prior probabilities. It is “objectively rational” to choose f in the presence of g if and only if the expected utility of f is at least as high as that of g given each and every prior in the set. It is “subjectively rational” to choose f rather than g if and only if the minimal expected utility of f (relative to all priors in the set) is at least as high as that of g.Rationality, Multiple Priors.
Guarded Teams: The Horizontally Guarded Case
Team semantics admits reasoning about large sets of data, modelled by sets of assignments (called teams), with first-order syntax. This leads to high expressive power and complexity, particularly in the presence of atomic dependency properties for such data sets. It is therefore interesting to explore fragments and variants of logic with team semantics that permit model-theoretic tools and algorithmic methods to control this explosion in expressive power and complexity.
We combine here the study of team semantics with the notion of guarded logics, which are well-understood in the case of classical Tarski semantics, and known to strike a good balance between expressive power and algorithmic manageability. In fact there are two strains of guardedness for teams. Horizontal guardedness requires the individual assignments of the team to be guarded in the usual sense of guarded logics. Vertical guardedness, on the other hand, posits an additional (or definable) hypergraph structure on relational structures in order to interpret a constraint on the component-wise variability of assignments within teams.
In this paper we investigate the horizontally guarded case. We study horizontally guarded logics for teams and appropriate notions of guarded team bisimulation. In particular, we establish characterisation theorems that relate invariance under guarded team bisimulation with guarded team logics, but also with logics under classical Tarski semantics
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