docs: add a section on Why TensorInference.jl on the welcome page

Author: mroavi

docs/src/index.md

@@ -24,6 +24,38 @@ Solutions to the most common probabilistic inference tasks, including:
 - **Marginal Maximum a Posteriori (MMAP)**: Finds the most probable state of a
   subset of variables, averaging out the uncertainty over the remaining ones.
 
+## Why TensorInference.jl
+
+A major challenge in developing intelligent systems is the ability to reason
+under uncertainty, a challenge that appears in many real-world problems across
+various domains, including artificial intelligence, medical diagnosis,
+computer vision, computational biology, and natural language processing.
+Reasoning under uncertainty involves calculating the probabilities of relevant
+variables while taking into account any information that is acquired. This
+process, which can be thought of as drawing global insights from local
+observations, is known as *probabilistic inference*.
+
+*Probabilistic graphical models* (PGMs) provide a unified framework to perform
+probabilistic inference. These models use graphs to represent the joint
+probability distribution of complex systems in a concise manner by exploiting
+the conditional independence between variables in the model. Additionally,
+they form the foundation for various algorithms that enable efficient
+probabilistic inference.
+
+However, even with the representational aid of PGMs, performing probabilistic
+inference remains an intractable endeavor on many real-world models. The
+reason is that performing probabilistic inference involves complex
+combinatorial optimization problems in very high dimensional spaces. To tackle
+these challenges, more efficient and scalable inference algorithms are needed.
+
+As an attempt to tackle the aforementioned challenges, we present
+`TensorInference.jl`, a Julia package for probabilistic inference that
+combines the representational capabilities of PGMs with the computational
+power of tensor networks. By harnessing the best of both worlds,
+`TensorInference.jl` aims to enhance the performance of probabilistic
+inference, thereby expanding the tractability spectrum of exact inference for
+more complex, real-world models.
+
 ## Outline
 ```@contents
 Pages = [