4,521 research outputs found
A psychoacoustic model of harmonic cadences: a preliminary report
This report presents a psychoacoustically derived computational model of the perceived distance between any two major or minor triads, the degree of activity created by any given pair of triads, and the cadential effectiveness of three-triad progressions. It also provides statistical analyses of the ratings given by thirty-five participants for the "similarity" and "fit" of triads in a pair, and the "cadential effectiveness" of three-triad progressions. Multiple regressions show that the model provides highly significant predictions of the experimentally obtained ratings. Finally, it is argued that because the model is based upon psychoacoustic axioms, it is likely the regression equations represent true causal models. As such, the computational model and its associated theory question the plausibility of theoretical approaches to tonality that use only long-term memory and statistical features, as well as those approaches based upon symmetrical geometrical structures like the torus. It is hoped that the psychoacoustic approach proposed here may herald not only the return of psychoacoustic approaches to tonal music theory, but also the exploration of the tonal possibilities offered by non-standard tunings and non-harmonic timbres
Generalized Independent Noise Condition for Estimating Causal Structure with Latent Variables
We investigate the challenging task of learning causal structure in the
presence of latent variables, including locating latent variables and
determining their quantity, and identifying causal relationships among both
latent and observed variables. To address this, we propose a Generalized
Independent Noise (GIN) condition for linear non-Gaussian acyclic causal models
that incorporate latent variables, which establishes the independence between a
linear combination of certain measured variables and some other measured
variables. Specifically, for two observed random vectors and ,
GIN holds if and only if and are
independent, where is a non-zero parameter vector determined by the
cross-covariance between and . We then give necessary
and sufficient graphical criteria of the GIN condition in linear non-Gaussian
acyclic causal models. Roughly speaking, GIN implies the existence of an
exogenous set relative to the parent set of (w.r.t.
the causal ordering), such that d-separates from
. Interestingly, we find that the independent noise condition
(i.e., if there is no confounder, causes are independent of the residual
derived from regressing the effect on the causes) can be seen as a special case
of GIN. With such a connection between GIN and latent causal structures, we
further leverage the proposed GIN condition, together with a well-designed
search procedure, to efficiently estimate Linear, Non-Gaussian Latent
Hierarchical Models (LiNGLaHs), where latent confounders may also be causally
related and may even follow a hierarchical structure. We show that the
underlying causal structure of a LiNGLaH is identifiable in light of GIN
conditions under mild assumptions. Experimental results show the effectiveness
of the proposed approach
Identifiable Latent Polynomial Causal Models Through the Lens of Change
Causal representation learning aims to unveil latent high-level causal
representations from observed low-level data. One of its primary tasks is to
provide reliable assurance of identifying these latent causal models, known as
identifiability. A recent breakthrough explores identifiability by leveraging
the change of causal influences among latent causal variables across multiple
environments \citep{liu2022identifying}. However, this progress rests on the
assumption that the causal relationships among latent causal variables adhere
strictly to linear Gaussian models. In this paper, we extend the scope of
latent causal models to involve nonlinear causal relationships, represented by
polynomial models, and general noise distributions conforming to the
exponential family. Additionally, we investigate the necessity of imposing
changes on all causal parameters and present partial identifiability results
when part of them remains unchanged. Further, we propose a novel empirical
estimation method, grounded in our theoretical finding, that enables learning
consistent latent causal representations. Our experimental results, obtained
from both synthetic and real-world data, validate our theoretical contributions
concerning identifiability and consistency
Identification of Nonlinear Latent Hierarchical Models
Identifying latent variables and causal structures from observational data is
essential to many real-world applications involving biological data, medical
data, and unstructured data such as images and languages. However, this task
can be highly challenging, especially when observed variables are generated by
causally related latent variables and the relationships are nonlinear. In this
work, we investigate the identification problem for nonlinear latent
hierarchical causal models in which observed variables are generated by a set
of causally related latent variables, and some latent variables may not have
observed children.
We show that the identifiability of causal structures and latent variables
(up to invertible transformations) can be achieved under mild assumptions: on
causal structures, we allow for multiple paths between any pair of variables in
the graph, which relaxes latent tree assumptions in prior work; on structural
functions, we permit general nonlinearity and multi-dimensional continuous
variables, alleviating existing work's parametric assumptions. Specifically, we
first develop an identification criterion in the form of novel identifiability
guarantees for an elementary latent variable model. Leveraging this criterion,
we show that both causal structures and latent variables of the hierarchical
model can be identified asymptotically by explicitly constructing an estimation
procedure. To the best of our knowledge, our work is the first to establish
identifiability guarantees for both causal structures and latent variables in
nonlinear latent hierarchical models.Comment: NeurIPS 202
A Survey on Causal Discovery Methods for Temporal and Non-Temporal Data
Causal Discovery (CD) is the process of identifying the cause-effect
relationships among the variables from data. Over the years, several methods
have been developed primarily based on the statistical properties of data to
uncover the underlying causal mechanism. In this study we introduce the common
terminologies in causal discovery, and provide a comprehensive discussion of
the approaches designed to identify the causal edges in different settings. We
further discuss some of the benchmark datasets available for evaluating the
performance of the causal discovery algorithms, available tools to perform
causal discovery readily, and the common metrics used to evaluate these
methods. Finally, we conclude by presenting the common challenges involved in
CD and also, discuss the applications of CD in multiple areas of interest
Linear Causal Disentanglement via Interventions
Causal disentanglement seeks a representation of data involving latent
variables that relate to one another via a causal model. A representation is
identifiable if both the latent model and the transformation from latent to
observed variables are unique. In this paper, we study observed variables that
are a linear transformation of a linear latent causal model. Data from
interventions are necessary for identifiability: if one latent variable is
missing an intervention, we show that there exist distinct models that cannot
be distinguished. Conversely, we show that a single intervention on each latent
variable is sufficient for identifiability. Our proof uses a generalization of
the RQ decomposition of a matrix that replaces the usual orthogonal and upper
triangular conditions with analogues depending on a partial order on the rows
of the matrix, with partial order determined by a latent causal model. We
corroborate our theoretical results with a method for causal disentanglement
that accurately recovers a latent causal model
Nonparametric Identifiability of Causal Representations from Unknown Interventions
We study causal representation learning, the task of inferring latent causal
variables and their causal relations from high-dimensional functions
("mixtures") of the variables. Prior work relies on weak supervision, in the
form of counterfactual pre- and post-intervention views or temporal structure;
places restrictive assumptions, such as linearity, on the mixing function or
latent causal model; or requires partial knowledge of the generative process,
such as the causal graph or the intervention targets. We instead consider the
general setting in which both the causal model and the mixing function are
nonparametric. The learning signal takes the form of multiple datasets, or
environments, arising from unknown interventions in the underlying causal
model. Our goal is to identify both the ground truth latents and their causal
graph up to a set of ambiguities which we show to be irresolvable from
interventional data. We study the fundamental setting of two causal variables
and prove that the observational distribution and one perfect intervention per
node suffice for identifiability, subject to a genericity condition. This
condition rules out spurious solutions that involve fine-tuning of the
intervened and observational distributions, mirroring similar conditions for
nonlinear cause-effect inference. For an arbitrary number of variables, we show
that two distinct paired perfect interventions per node guarantee
identifiability. Further, we demonstrate that the strengths of causal
influences among the latent variables are preserved by all equivalent
solutions, rendering the inferred representation appropriate for drawing causal
conclusions from new data. Our study provides the first identifiability results
for the general nonparametric setting with unknown interventions, and
elucidates what is possible and impossible for causal representation learning
without more direct supervision
A semiotic analysis of the genetic information
Terms loaded with informational connotations are often employed to refer to genes and their dynamics. Indeed, genes are usually perceived by biologists as basically ‘the carriers of hereditary information.’ Nevertheless, a number of researchers consider such talk as inadequate and ‘just metaphorical,’ thus expressing a skepticism about the use of the term ‘information’ and its derivatives in biology as a natural science. First, because the meaning of that term in biology is not as precise as it is, for instance, in the mathematical theory of communication. Second, because it seems to refer to a purported semantic property of genes without theoretically clarifying if any genuinely intrinsic semantics is involved. Biosemiotics, a field that attempts to analyze biological systems as semiotic systems, makes it possible to advance in the understanding of the concept of information in biology. From the perspective of Peircean biosemiotics, we develop here an account of genes as signs, including a detailed analysis of two fundamental processes in the genetic information system (transcription and protein synthesis) that have not been made so far in this field of research. Furthermore, we propose here an account of information based on Peircean semiotics and apply it to our analysis of transcription and protein synthesis
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