Deep neural networks (DNNs) have garnered significant attention in financial asset pricing, due to their strong capacity for modeling complex nonlinear relationships within financial data. However, sophisticated models are prone to over-fitting to the noise information in financial data, resulting in inferior performance. To address this issue, we propose an information bottleneck asset pricing model that compresses data with low signal-to-noise ratios to eliminate redundant information and retain the critical information for asset pricing. Our model imposes constraints of mutual information during the nonlinear mapping process. Specifically, we progressively reduce the mutual information between the input data and the compressed representation while increasing the mutual information between the compressed representation and the output prediction. The design ensures that irrelevant information, which is essentially the noise in the data, is forgotten during the modeling of financial nonlinear relationships without affecting the final asset pricing. By leveraging the constraints of the Information bottleneck, our model not only harnesses the nonlinear modeling capabilities of deep networks to capture the intricate relationships within financial data but also ensures that noise information is filtered out during the information compression process.

We introduce a new, non-parametric and principled, distance based clustering method. This method combines a pairwise based ap(cid:173) proach with a vector-quantization method which provide a mean(cid:173) ingful interpretation to the resulting clusters. The idea is based on turning the distance matrix into a Markov process and then examine the decay of mutual-information during the relaxation of this process. The clusters emerge as quasi-stable structures dur(cid:173) ing this relaxation, and then are extracted using the information bottleneck method. The method can cluster data with no geometric or other bias and makes no assumption about the underlying distribution.

We argue that K–means and deterministic annealing algorithms for geo- metric clustering can be derived from the more general Information Bot- tleneck approach. If we cluster the identities of data points to preserve information about their location, the set of optimal solutions is massively degenerate. But if we treat the equations that define the optimal solution as an iterative algorithm, then a set of "smooth" initial conditions selects solutions with the desired geometrical properties. In addition to concep- tual unification, we argue that this approach can be more efficient and robust than classic algorithms.

Many real-world multi-agent reinforcement learning applications require agents to communicate, assisted by a communication protocol. These applications face a common and critical issue of communication's limited bandwidth that constrains agents' ability to cooperate successfully. In this paper, rather than proposing a fixed communication protocol, we develop an Informative Multi-Agent Communication (IMAC) method to learn efficient communication protocols. Our contributions are threefold. First, we notice a fact that a limited bandwidth translates into a constraint on the communicated message entropy, thus paving the way of controlling the bandwidth. Second, we introduce a customized batch-norm layer, which controls the messages' entropy to simulate the limited bandwidth constraint. Third, we apply the information bottleneck method to discover the optimal communication protocol, which can satisfy a bandwidth constraint via training with the prior distribution in the method. To demonstrate the efficacy of our method, we conduct extensive experiments in various cooperative and competitive multi-agent tasks across two dimensions: the number of agents and different bandwidths. We show that IMAC converges fast, and leads to efficient communication among agents under the limited-bandwidth constraint as compared to many baseline methods.

The Information bottleneck method is an unsupervised non-parametric data organization technique. Given a joint distribution P(A,B), this method constructs a new variable T that extracts partitions, or clusters, over the values of A that are informative about B. The information bottleneck has already been applied to document classification, gene expression, neural code, and spectral analysis. In this paper, we introduce a general principled framework for multivariate extensions of the information bottleneck method. This allows us to consider multiple systems of data partitions that are inter-related. Our approach utilizes Bayesian networks for specifying the systems of clusters and what information each captures. We show that this construction provides insight about bottleneck variations and enables us to characterize solutions of these variations. We also present a general framework for iterative algorithms for constructing solutions, and apply it to several examples.

We present a general model-independent approach to the analysis of data in cases when these data do not appear in the form of co-occurrence of two variables X,Y, but rather as a sample of values of an unknown (stochastic) function Z(X,Y). For example, in gene expression data, the expression level Z is a function of gene X and condition Y; or in movie ratings data the rating Z is a function of viewer X and movie Y. The approach represents a consistent extension of the Information Bottleneck method that has previously relied on the availability of co-occurrence statistics. By altering the relevance variable we eliminate the need in the sample of joint distribution of all input variables. This new formulation also enables simple MDL-like model complexity control and prediction of missing values of Z. The approach is analyzed and shown to be on a par with the best known clustering algorithms for a wide range of domains. For the prediction of missing values (collaborative filtering) it improves the currently best known results.

We present a general model-independent approach to the analysis of data in cases when these data do not appear in the form of co-occurrence of two variables X,Y, but rather as a sample of values of an unknown (stochastic) function Z(X,Y). For example, in gene expression data, the expression level Z is a function of gene X and condition Y; or in movie ratings data the rating Z is a function of viewer X and movie Y. The approach represents a consistent extension of the Information Bottleneck method that has previously relied on the availability of co-occurrence statistics. By altering the relevance variable we eliminate the need in the sample of joint distribution of all input variables. This new formulation also enables simple MDL-like model complexity control and prediction of missing values of Z. The approach is analyzed and shown to be on a par with the best known clustering algorithms for a wide range of domains. For the prediction of missing values (collaborative filtering) it improves the currently best known results.

We present a general model-independent approach to the analysis of data in cases when these data do not appear in the form of co-occurrence of two variables X,Y, but rather as a sample of values of an unknown (stochastic) function Z(X,Y). For example, in gene expression data, the expression level Z is a function of gene X and condition Y; or in movie ratings data the rating Z is a function of viewer X and movie Y . The approach represents a consistent extension of the Information Bottleneck method that has previously relied on the availability of co-occurrence statistics. By altering the relevance variable we eliminate the need in the sample of joint distribution of all input variables. This new formulation also enables simple MDL-like model complexity control and prediction of missing values of Z. The approach is analyzed and shown to be on a par with the best known clustering algorithms for a wide range of domains. For the prediction of missing values (collaborative filtering) it improves the currently best known results.

We argue that K-means and deterministic annealing algorithms for geometric clustering can be derived from the more general Information Bottleneck approach. If we cluster the identities of data points to preserve information about their location, the set of optimal solutions is massively degenerate. But if we treat the equations that define the optimal solution as an iterative algorithm, then a set of "smooth" initial conditions selects solutions with the desired geometrical properties. In addition to conceptual unification, we argue that this approach can be more efficient and robust than classic algorithms.

We argue that K-means and deterministic annealing algorithms for geometric clustering can be derived from the more general Information Bottleneck approach. If we cluster the identities of data points to preserve information about their location, the set of optimal solutions is massively degenerate. But if we treat the equations that define the optimal solution as an iterative algorithm, then a set of "smooth" initial conditions selects solutions with the desired geometrical properties. In addition to conceptual unification, we argue that this approach can be more efficient and robust than classic algorithms.