it's the weekend....

be girly.

*images courtesy of v., coco and kelley, eileen kathryn boyd, raina kattelson, mrs. blandings

On MRF factorization

Recently, I figured out I didn't understand two simple things about MRFs:

1. When we are talking about MRF factorization, in the formulation of the likelihood

   
   should we consider all the cliques in the network or only maximal ones?
2. Generally, why do we have a right to factorize the likelihood this way?

I asked some folks, and it turned out that nobody understood this basic property clearly (In spite of Dmitry Vetrov assured me he had explained that fact in his courses). Finally, I've found the answers in Christopher Bishop's book. If you are not familiar with Markov Random Fields or graphical models, I recommend you to read the book, it is relatively understandable.

So, let's start with the second question. For those of you who like names, it is exactly the necessity part of the Hammersley-Clifford theorem. As Bishop put it:

If we consider two nodes x_i and x_j that are not connected by a link, then these variables must be conditionally independent given all other nodes in the graph. This follows from the fact that there is no direct path between the two nodes, and all other paths pass through nodes that are observed, and hence those paths are blocked. This conditional independence property can be expressed as

where x_\{i,j} denotes the set x of all variables with x_i and x_j removed. The factorization of the joint distribution must therefore be such that x_i and x_j do not appear in the same factor in order for the conditional independence property to hold for all possible distributions belonging to the graph.

One could find the answer to the first question in Bishop's book as well. Normally, we should include all the cliques to the product. Actually, every function of variables X is also a function of any Y that is a superset of X. Based on that, a potential for a non-maximal clique could be merged into a potential for any maximal clique such that it is a supergraph of the first clique! Thus, both formulations (with all cliques and only maximal cliques) are equally expressive.

camouflage

there is a paint color by ben moore that i am totally in love with called camouflage (2143-40). it is a beautiful soft green without screaming "green". i used it on the exterior of a beach house along with the accent color, alexandria beige (HC-77). these images remind me of how pretty this color is.

*images courtesy of mod girl, martha stewart living, house and home, southern accents

"me time"

have you ever suffered from pregnancy meltdowns (where you turn completely crazy for no apparent reason)? i had one last night....it was caused by the library calling to tell me to return "elmo's potty time" for the second time. i sat on the couch and shed some tears and said i need some "me time". it lasted about ten minutes...then i felt silly and ate ice cream.

ha....being pregnant- isn't it grand :)

*images courtesy of coco cozy, house of turquoise/atlanta home magazine, real simple (bottom two images)

The Body Fat Setpoint, Part III: Dietary Causes of Obesity

[2013 update: I've edited this post to remove elements that I feel were poorly supported.  I now think that changes in the setpoint are at least partially secondary to passive overconsumption of calories, particularly low quality calories]

What Caused the Setpoint to Change?

We have two criteria to narrow our search for the cause of modern fat gain:

1. It has to be new to the human environment
2. At some point, it has to cause leptin resistance or otherwise disturb the setpoint

Although I believe that exercise is part of a healthy lifestyle, and can help prevent fat gain and to some degree treat overweight, it probably can't explain the recent increase in fat mass in modern nations. This is because exercise doesn't appear to have declined. There are various other possible explanations, such as industrial pollutants, a lack of sleep and psychological stress, which may play a role. But I feel that diet is likely to be the primary cause. When you're drinking 20 oz Cokes, bisphenol-A contamination is the least of your worries.

In the last post, I described two mechanisms that may contribute to elevating the body fat set point by causing leptin resistance: inflammation in the hypothalamus, and impaired leptin transport into the brain due to elevated triglycerides. After more reading and discussing it with my mentor, I've decided that the triglyceride hypothesis is on shaky ground*. Nevertheless, it is consistent with certain observations:

• Fibrate drugs that lower triglycerides can lower fat mass in rodents and humans
• Low-carbohydrate diets are somewhat effective for fat loss and lower triglycerides
• Fructose can cause leptin resistance in rodents and it elevates triglycerides (1)
• Fish oil reduces triglycerides. Some but not all studies have shown that fish oil aids fat loss (2)

Inflammation in the hypothalamus, with accompanying resistance to leptin signaling, has been reported in a number of animal studies of diet-induced obesity. I feel it's likely to occur in humans as well, although the dietary causes are probably different for humans. The hypothalamus is the primary site where leptin acts to regulate fat mass (3). Importantly, preventing inflammation in the brain prevents leptin resistance and obesity in diet-induced obese mice (3.1). The hypothalamus is likely to be the most important site of action. Research is underway on this.

The Role of Digestive Health

What causes inflammation in the hypothalamus? One of the most interesting hypotheses is that increased intestinal permeability allows inflammatory substances to cross into the circulation from the gut, irritating a number of tissues including the hypothalamus.

Dr. Remy Burcelin and his group have spearheaded this research. They've shown that high-fat diets cause obesity in mice, and that they also increase the level of an inflammatory substance called lipopolysaccharide (LPS) in the blood. LPS is produced by gram-negative bacteria in the gut and is one of the main factors that activates the immune system during an infection. Antibiotics that kill gram-negative bacteria in the gut prevent the negative consequences of high-fat feeding in mice.

Burcelin's group showed that infusing LPS into mice on a low-fat chow diet causes them to become obese and insulin resistant just like high-fat fed mice (4). Furthermore, adding 10% of the soluble fiber oligofructose to the high-fat diet prevented the increase in intestinal permeability and also largely prevented the body fat gain and insulin resistance from high-fat feeding (5). Oligofructose is food for friendly gut bacteria and ends up being converted to butyrate and other short-chain fatty acids in the colon. This results in lower intestinal permeability to toxins such as LPS. This is particularly interesting because oligofructose supplements cause fat loss in humans (6).

A recent study showed that blood LPS levels are correlated with body fat, elevated cholesterol and triglycerides, and insulin resistance in humans (7). However, a separate study didn't come to the same conclusion (8). The discrepancy may be due to the fact that LPS isn't the only inflammatory substance to cross the gut lining-- other substances may also be involved. Anything in the blood that shouldn't be there is potentially inflammatory.

Overall, I think gut dysfunction could play a role in obesity and other modern metabolic problems.
Exiting the Niche

I believe that we have strayed too far from our species' ecological niche, and our health is suffering. One manifestation of that is body fat gain. Many factors probably contribute, but I believe that diet is the most important. A diet heavy in nutrient-poor refined carbohydrates and industrial omega-6 oils, high in gut irritating substances such as gluten and sugar, and a lack of direct sunlight, have caused us to lose the robust digestion and good micronutrient status that characterized our distant ancestors. I believe that one consequence has been the dysregulation of the system that maintains the fat mass "setpoint". This has resulted in an increase in body fat in 20th century affluent nations, and other cultures eating our industrial food products.

In the next post, I'll discuss my thoughts on how to reset the body fat setpoint.

* The ratio of leptin in the serum to leptin in the brain is diminished in obesity, but given that serum leptin is very high in the obese, the absolute level of leptin in the brain is typically not lower than a lean person. Leptin is transported into the brain by a transport mechanism that saturates when serum leptin is not that much higher than the normal level for a lean person. Therefore, the fact that the ratio of serum to brain leptin is higher in the obese does not necessarily reflect a defect in transport, but rather the fact that the mechanism that transports leptin is already at full capacity.