Symbolic data analysis (SDA) is an emerging area of statistics concerned with understanding and modelling data that takes distributional form (i.e. symbols), such as random lists, intervals and histograms. It was developed under the premise that the statistical unit of interest is the symbol, and that inference is requ…
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48 results for “Symbol analysis”
How can neural networks perform so well on compositional tasks even though they lack explicit compositional representations? We use a novel analysis technique called ROLE to show that recurrent neural networks perform well on such tasks by converging to solutions which implicitly represent symbolic structure. This meth…
Enhances Cox model for survival analysis with symbolic non-linear log-risk functions.
problem Limited interpretability and non-linearity in traditional Cox models.
method Introduces GCPH model using Kolmogorov-Arnold Networks for symbolic non-linear log-risk functions.
result GCPH achieves competitive performance and superior interpretability.
Study connects boundary geometry to symbol of Dirichlet-to-Neumann operator.
problem Determining geometric data from boundary symbol of connection Laplacian.
method Analyze symbol of Dirichlet-to-Neumann operator associated with connection Laplacian.
result Geometric data on boundary and normal derivatives are determined by symbol.
MusPy is a toolkit for symbolic music generation, providing tools for dataset management and analysis.
problem Facilitating the creation and analysis of symbolic music datasets.
method Development of an open-source Python library (MusPy) with features for dataset management, data I/O, preprocessing, and model evaluation. Demonstrated through statistical analysis and cross-dataset generalizability experiments.
result MusPy's dataset analysis reveals varying degrees of cross-genre representation across different music datasets.
The symbolic dynamics technique is well-known for low-dimensional dynamical systems and chaotic maps, and lies at the roots of the thermodynamic formalism of dynamical systems. Here we show that this technique can also be successfully applied to time series generated by complex systems of much higher dimensionality. Ou…
Study evaluates clustering methods for Google Trends data.
problem Clustering high-dimensional, noisy time series data.
method Symbolic Aggregate Approximation (SAX), Enhanced SAX (eSAX), and Topological Data Analysis (TDA).
result TDA provides more balanced and meaningful groupings than SAX and eSAX.
Not All Neuro-Symbolic Concepts Are Created Equal: Analysis and Mitigation of Reasoning Shortcutscs.LG
This work identifies and mitigates reasoning shortcuts in Neuro-Symbolic models.
problem Neuro-Symbolic models can achieve high accuracy by using unintended concepts.
method Characterized reasoning shortcuts as unintended optima of the learning objective and identified four key conditions.
result Reasoning shortcuts are difficult to mitigate, casting doubt on NeSy solutions' trustworthiness and interpretability.
This work analyzes tree-based methods from a ranking perspective, providing insights and new statistics.
problem Understanding the effectiveness of tree-based methods in finite-sample settings, especially symbolic feature selection.
method Local ranking perspective, finite-sample analysis, oracle bounds, posterior contraction results, concordant divergence statistics.
result New insights and statistics for evaluating symbolic feature mappings.
NEMoTS improves time series analysis by deriving efficient, interpretable models.
problem Lack of comprehensive understanding and insightful explanations in time series analysis.
method Neural-enhanced Monte-Carlo Tree Search (NEMoTS) for symbolic regression.
result NEMoTS provides efficient and interpretable models for time series analysis.
The paper models musical motif transformations in Beethoven's works.
problem Understanding how motifs transform in symbolic music.
method Developed a probabilistic framework using Conditional Random Fields.
result Identified patterns of motif transformations and their co-occurrences.
Paper analyzes symbolic-dynamics inspired Markov modeling for time-series data.
problem Capturing temporal patterns in sequential data for statistical learning.
method Two-step process: discretization of continuous attributes and estimation of temporal memory.
result Effective Markov modeling depends on accurate discretization and memory estimation.
Zoetrope Genetic Programming improves symbolic regression performance.
problem Evolutionary symbolic regression for complex mathematical expressions.
method Zoetropic representation, repeated fusion operations, linear combination, crossover, mutation, selection.
result Zoetrope Genetic Programming achieves state-of-the-art performance and low computational time.
Analysis and manipulation of trained neural networks is a challenging and important problem. We propose a symbolic representation for piecewise-linear neural networks and discuss its efficient computation. With this representation, one can translate the problem of analyzing a complex neural network into that of analyzi…
PandaAI: A practical agent for neuro-symbolic data analysis and decision-making in finance
problem Sequential decision-making in finance
method Leveraging LLMs for market regime modeling and constrained alpha generation
result PandaAI achieves higher Rank IC and lower maximum drawdown
We show that the Borel sums of the Voros symbols considered in the theory of exact WKB analysis arise naturally as Fock-Goncharov coordinates of framed -local systems on a marked bordered surface. Using this result, we show that these Borel sums can be meromorphically continued to any point of $\math…
The Atiyah-Singer index theorem is a topological formula for the index of an elliptic differential operator. The topological index depends on a cohomology class that is constructed from the principal symbol of the operator. On contact manifolds, the important Fredholm operators are not elliptic, but hypoelliptic. Their…
Deep neural network generates symbolic equations from data.
problem Lack of insight into underlying mappings from traditional deep learning.
method Combines deep learning flexibility with symbolic solutions.
result Accurately generates governing equations for dynamical systems.
In order to build efficient deep recurrent neural architectures, it is essential to analyze the complexityof long distance dependencies (LDDs) of the dataset being modeled. In this paper, we presentdetailed analysis of the dependency decay curve exhibited by various datasets. The datasets sampledfrom a similar process …
Neuro-symbolic traders suppress market prices, highlighting risks to stability.
problem Understanding and quantifying the influence of AI-generated financial models on markets.
method Developed virtual neuro-symbolic traders using deep generative models and tested them in a virtual market.
result Neuro-symbolic traders suppress market prices compared to historical data, indicating potential market instability.
The paper explores states of financial markets using correlation matrices and their dynamics.
problem Understanding the states of financial markets based on correlations.
method Revisits previous work and introduces recent developments in practical applications.
result Analysis of trajectories and symbolic dynamics in correlation matrix space.
A hybrid algorithm combines optimization and enumeration for symbolic regression.
problem Finding any function from a set of operators without prior specification.
method Mixed-integer nonlinear optimization with explicit enumeration and constraints.
result The hybrid algorithm is competitive with state-of-the-art methods.
VaSST uses soft symbolic trees for probabilistic symbolic regression.
problem Efficiently recover symbolic expressions from noisy data.
method Variational inference with soft symbolic trees.
result Superior performance in structural recovery and predictive accuracy.
In this paper we give formulae for the Dixmier trace and the noncommutative residue (also called Wodzicki's residue) of pseudo-differential operators by using the notion of global symbol. We consider both cases, compact manifolds with or without boundary. Our analysis on the Dixmier trace of invariant pseudo-differenti…
Opening the Black-Box: Symbolic Regression with Kolmogorov-Arnold Networks for Energy Applicationscs.LG
Kolmogorov-Arnold Networks offer interpretable models for energy applications.
problem Lack of interpretability in modern machine learning methods for sensitive industries.
method Symbolic regression with Kolmogorov-Arnold Networks compared to traditional feedforward neural networks.
result Kolmogorov-Arnold Networks yield perfectly interpretable models and learn real, physical relations.
We present a novel certified and complete algorithm to compute arrangements of real planar algebraic curves. It provides a geometric-topological analysis of the decomposition of the plane induced by a finite number of algebraic curves in terms of a cylindrical algebraic decomposition. From a high-level perspective, the…
Paper develops a framework to discover bioprocessing regulatory mechanisms using symbolic and statistical learning.
problem Challenges in modeling complex intracellular regulation, stochastic system behavior, and limited experimental data.
method Symbolic and statistical learning framework based on stochastic differential equations and Bayesian learning.
result Improved sample efficiency and robust model selection compared to state-of-the-art approaches.
Explores tensor products in hyperdimensional computing.
problem Understanding tensor products in hyperdimensional computing.
method Generalized results from graph embeddings to vector symbolic architectures and hyperdimensional computing.
result Tensor product is the most general and expressive representation with errorless unbinding and detection.
We describe dimensionally constrained symbolic regression which has been developed for mass measurement in certain classes of events in high-energy physics (HEP). With symbolic regression, we can derive equations that are well known in HEP. However, in problems with large number of variables, we find that by constraini…
Paper closes neural-symbolic learning loop with grammar model and back-search algorithm.
problem Slow convergence in neural-symbolic learning due to error propagation issues.
method Introduces grammar model as symbolic prior and back-search algorithm for efficient error propagation.
result Significantly outperforms RL methods in performance, converging speed, and data efficiency.
This paper presents a technique for reduced-order Markov modeling for compact representation of time-series data. In this work, symbolic dynamics-based tools have been used to infer an approximate generative Markov model. The time-series data are first symbolized by partitioning the continuous measurement space of the …
Reinforcement learning and symbolic planning have both been used to build intelligent autonomous agents. Reinforcement learning relies on learning from interactions with real world, which often requires an unfeasibly large amount of experience. Symbolic planning relies on manually crafted symbolic knowledge, which may …
The paper proposes a method to compute higher infinitesimals in numerical and symbolic analysis.
problem Computing higher-order derivatives with higher infinitesimals.
method Automatic differentiation in terms of C-infinity rings and Weil algebras.
result A unifying theoretical framework for multivariate higher-order derivatives.
For an arbitrary Riemannian manifold and Hermitian vector bundles and over we define the notion of the normal symbol of a pseudodifferential operator from to . The normal symbol of is a certain smooth function from the cotangent bundle to the homomorphism bundle and dep…
Extends Fisher's Discriminant Analysis for interval-valued data.
problem Classifying entities represented by intervals and histograms.
method Adapts Fisher's Discriminant Analysis using Moore's interval arithmetic and Mallows' distance.
result Discriminant directions for interval-valued data are numerically maximized.
Based on the ideas of Optimal Control, we introduce the new basic characteristic of a bracket generating distribution, the Jacobi symbol. In contrast to the classical Tanaka symbol, the set of Jacobi symbols is discrete and classifiable. We give an explicit and unified algebraic procedure for the construction of the ca…
Discover equations of motion from distorted video frames.
problem Learning equations of motion from unlabeled, distorted video.
method Train an autoencoder to map frames into latent space, then use symbolic regression to find differential equations.
result The method can discover motion equations even when video is distorted.
Reinforcement learning algorithms can solve dynamic decision-making and optimal control problems. With continuous-valued state and input variables, reinforcement learning algorithms must rely on function approximators to represent the value function and policy mappings. Commonly used numerical approximators, such as ne…
A method for making machine learning units-equivariant using dimensional analysis.
problem Ensuring machine learning models respect dimensional consistency.
method Constructing dimensionless inputs and applying equivariant machine learning methods.
result Improved accuracy in tasks requiring dimensional consistency.
ECSEL learns signomial equations for explainable classification.
problem Creating interpretable models for classification.
method ECSEL constructs signomial equations directly for classification and explanation.
result ECSEL outperforms state-of-the-art methods in interpretability and efficiency.
In this paper, we consider the problem of fast and efficient indexing techniques for sequences evolving in non-Euclidean spaces. This problem has several applications in the areas of human activity analysis, where there is a need to perform fast search, and recognition in very high dimensional spaces. The problem is ma…
Network node embedding is an active research subfield of complex network analysis. This paper contributes a novel approach to learning network node embeddings and direct node classification using a node ranking scheme coupled with an autoencoder-based neural network architecture. The main advantages of the proposed Dee…
Global analysis of Dixmier traces and Wodzicki residues on compact Lie groups.
problem Computing Dixmier traces and Wodzicki residues on compact Lie groups.
method Global quantisation approach, using global symbols and representation theory.
result Explicit formulae for Dixmier traces and Wodzicki residues on compact Lie groups.
On mod 3 triple Milnor invariants and triple cubic residue symbols in the Eisenstein number fieldmath.NT
We introduce mod 3 triple Milnor invariants and triple cubic residue symbols for certain primes of the Eisenstein number field , following the analogies between knots and primes. Our triple symbol generalizes both the cubic residue symbol and Rédei's triple symbol, and describes the decomposition…
Symbolic Data Analysis is based on special descriptions of data - symbolic objects (SO). Such descriptions preserve more detailed information about units and their clusters than the usual representations with mean values. A special kind of symbolic object is a representation with frequency or probability distributions …
We introduce new tools for analytic microlocal analysis on Kähler manifolds. As an application, we prove that the space of Berezin-Toeplitz operators with analytic contravariant symbol is an algebra. We also give a short proof of the Bergman kernel asymptotics up to an exponentially small error.
A formula for Rademacher symbols in triangle groups is provided.
problem No specific problem stated; focuses on a mathematical formula.
method Presentation of an explicit formula for Rademacher symbols.
result Generalizes Ghys' proof of modular knot linking numbers.
Complex - symbols relate to hyperbolic tetrahedron volumes and determinants.
problem Analyzing asymptotics of complex - symbols.
method Relating asymptotics to hyperbolic tetrahedron volumes and determinants.
result Complex - symbols' asymptotics linked to tetrahedron volumes and determinants.